REVIEWING THE JOINT MOVEMENTS Name the motion in direction of arrow.
Thus far we’ve been talking about motion in the x direction independently from motion in the...
53
Thus far we’ve been talking about motion in the x direction independently from motion in the y- direction. In the real world motion occurs in a combination of Object Moving in the x Direction Object Falling in the y Direction Kinematic Equations Δx = V i t + ½at 2 V f 2 = V i 2 + 2aΔx V f = V i + at V ave = Δx/t V ave = (V i + V f ) / 2 a = (Vf – Vi) / t R = (V i 2 /g) sin(2θ)
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Transcript of Thus far we’ve been talking about motion in the x direction independently from motion in the...
Thus far wersquove been talking about motion in the x
direction independently from motion in the y-direction
In the real world motion occurs in a combination of
directions
Object Moving in the x Direction
Object Falling in the y DirectionKinematic Equations
Δx = Vit + frac12at2
Vf2
= Vi2 + 2aΔx
Vf = Vi + atVave = ΔxtVave = (Vi + Vf) 2a = (Vf ndash Vi) tR = (Vi
2g) sin(2θ)
Imagine trying to swim directly across a river that has a current flowing
perpendicular to your motion
Push a light box with 50N of force to the right and it moves to
the right
50N
Lift a light box with 50N of force
upwards and it moves up
50N
Lift and push a box at the same time and it will move to the right
and upward at the same time
50N
50N
The box moves in this direction
The red arrows graphically represent the magnitude
and direction of the applied forces and are called
component VECTORS
The black arrow is the RESULTANT vector It is a combination of the two
other vectors
50N
50N
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Imagine trying to swim directly across a river that has a current flowing
perpendicular to your motion
Push a light box with 50N of force to the right and it moves to
the right
50N
Lift a light box with 50N of force
upwards and it moves up
50N
Lift and push a box at the same time and it will move to the right
and upward at the same time
50N
50N
The box moves in this direction
The red arrows graphically represent the magnitude
and direction of the applied forces and are called
component VECTORS
The black arrow is the RESULTANT vector It is a combination of the two
other vectors
50N
50N
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Push a light box with 50N of force to the right and it moves to
the right
50N
Lift a light box with 50N of force
upwards and it moves up
50N
Lift and push a box at the same time and it will move to the right
and upward at the same time
50N
50N
The box moves in this direction
The red arrows graphically represent the magnitude
and direction of the applied forces and are called
component VECTORS
The black arrow is the RESULTANT vector It is a combination of the two
other vectors
50N
50N
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Lift a light box with 50N of force
upwards and it moves up
50N
Lift and push a box at the same time and it will move to the right
and upward at the same time
50N
50N
The box moves in this direction
The red arrows graphically represent the magnitude
and direction of the applied forces and are called
component VECTORS
The black arrow is the RESULTANT vector It is a combination of the two
other vectors
50N
50N
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Lift and push a box at the same time and it will move to the right
and upward at the same time
50N
50N
The box moves in this direction
The red arrows graphically represent the magnitude
and direction of the applied forces and are called
component VECTORS
The black arrow is the RESULTANT vector It is a combination of the two
other vectors
50N
50N
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
The red arrows graphically represent the magnitude
and direction of the applied forces and are called
component VECTORS
The black arrow is the RESULTANT vector It is a combination of the two
other vectors
50N
50N
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 50N Which direction does it move
N
S
EW
50N East
50N NorthNortheast
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
You are looking down on an orange box on a blue floor and it is being pulled to the east with a force of 50N while simultaneously being pulled North with a force of 25N Which direction does it move
N
S
EW
50N East
25N North
Because you are pulling stronger in an eastward direction the box will move more towards the east than the North
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
ldquoI go by Vector Its a mathematical term represented by an arrow with both direction and magnitude Vector Thats me because I commit crimes with both direction and magnitude Oh yeahrdquo The length of the arrow represents the magnitude and the direction
its pointed in represents the direction
A scalar is a quantity with magnitude only
SCALAR
Img via career pivot
Velocity Force Acceleration Displacement Momentum Time Mass Volume Temperature Length Speed
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A person briskly walks across a 10m room and halfway back in 5 seconds What is their average speed and average velocity
Room is 10 meters long
Speed is a scalar and uses total distance travelled It is not concerned with direction
Velocity is a vector an uses displacement It is concerned with direction
Displacement ne distance Displacement is how far you are from your initial position
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Determining the Resultant Vector of the two component vectors below
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
bull Hopefully you realize that since the two sides are equal in magnitude the angles must both be 45deg
bull We can use the Pythagorean theorem (A2 + B2 = C2) to determine the magnitude of the resultant or any of the Trig Functions
50N
50N50N
50N
RESULTANT
bull The Resultant is a simplification or combination of the other two vectorsbull Now you can do some trigonometry (SOHCAHTOA) and figure out magnitude
and direction of the resultant vector (I know this makes you happy)
45deg
45deg71N
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
2ms
25ms2ms
Determining the Resultant
Tail to Tip Method1) Start with any component vector2) Place the tail of any unused vector at the tip of it3) Connect the tail of the first vector to the tip of the last vector
25ms
This is not a right triangle so more information would be helpful
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
50N
50N50N
50N
RESULTANT
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Determining the Resultant Vector of the two component vectors below
Parallelogram Method1) The tail of both vectors originate at the same point2) Draw in your parallelogram3) The resultant vector goes from the tail of both vectors
to the opposite side
2ms
25ms
2ms
25ms
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Parallelogram 1) All angles must add up to 360deg2) Opposite Angles are Equal3) Opposite Sides are Equal
θ
θθ = θ
θ = θθ
θ
A
A
A = AB
B
B = BUse Law of Cosines to Calculate the Resultant
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
2ms
Graphical Method of Vector Resolution
1) Draw the vectors to scale with a ruler using tail to tip2) Draw in your resultant vector3) Measure its distance with a ruler and convert it back4) Use a protractor to determine the angle
4ms
2in
4in
45in
45in = 45ms
634deg
θ = Tan-1(42)
Check with trig
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
[1] Find the resultantVector 1 9m eastVector 2 8m north
[2] Find the resultantVector 1 4ms westVector 2 5ms south
[3] Find the resultantVector 1 10N westVector 2 6N eastVector 3 7N north
Vector Resolution ProblemsFor each problem draw the resultant using 1 the tail to tip method2 the parallelogram method3 graphically using a ruler and protractorDetermine the magnitude and direction using trigonometry
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A
100mCurrent
2ms
08ms
Tail to Tip
2ms
08ms
Resultant
Use Pythagorean theorem andor SOHCAHTOA to determine the magnitude and direction of the resultant vectorbull Tan-1 (OA) = Tan-1 (082) =218degbull Sin(218deg) = 08H thus H = 22ms
218deg
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant)
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A
100mCurrent
2ms
08ms
The current is pushing you downstream due East whereas you are swimming due north Your speed across the river is unaffected by the current since it has no impact on the North South Direction You are crossing the river at a speed of 08ms and it has it has a distance across of 100m This is a simple speed problem
S = dt so 08ms = 100mt
t = 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A
100mCurrent
2ms
08ms
Since we now know that your total time in the water was 125s and that that your rate downstream was 2ms we can very easily determine how far down stream you ended up
S = dt and d = st2ms x 125s = 250m
So the river pushes you downstream 250m in 125s
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d) At what angle should you swim to end up
directly across from a
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A
100m
2ms
08ms
Donrsquot misunderstand a resultantYour South to North component of motion (08ms) and your West to East component of motion (2ms) never changes The resultant is a combination of the two Its simply stating that the addition of both of those vectors results in a direction of motion that looks like the resultantBut you can still treat that motion individually as we just did
22ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A
100mCurrent
2ms
08ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms a) Determine the magnitude and direction of
your motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t = 125s
c) How far downstream do you end up d= 250md) At what angle should you swim to end up
directly across from a
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
A
100m 2ms08ms
This is a trick question You can NEVER reach the point directly across from A
The current is moving faster downstream than you can swim so even if you swam directly upstream the current would still win
The 08ms upstream would cancel with some of the 2ms and result in a vector of 12ms downstream
Resultant is 12ms
A river is 1000m wide and is flowing at rate of 20ms downstream You want to cross the river at point A and can swim at a rate of 080 ms How far downstream do you end up and how long does it take you cross the river a) Determine the magnitude and direction of your
motion with respect to the earth (get the Resultant) 22ms 218deg
b) How long does it take to cross the river t= 125sc) How far downstream do you end up 250md) At what angle should you swim to end up
directly across from a Impossible
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Breaking a Vector into Components
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
300ms
30deg
Use Sin to get y-component
Use Cos to get x-component
150msVy
260msVx
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Breaking a Vector into Components
300ms
30deg
150msVy
260msVx
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
The ball is going upwards initially at 15ms and will rise until gravity slows It to a complete stop at its highest point It will then fall and increase its velocity until it strikes the ground with the same magnitude it was launched with but in the opposite direction The only acceleration in the y direction is g (-10ms2) and we know initial and final velocity so we can figure out the time it will take the ball to land using
Vf = Vi +at -15ms = 15ms -10ms2 t
t = 3s
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
At its highest point the final velocity of the ball in the y direction will be 0 So we know initial and final velocity and acceleration and time if we cut the three seconds in half so there are several ways we could solve this
V2f = V2
i +2aΔy Vf = 0 Vi =15ms a = -10ms2
y = 113m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Breaking a Vector into Components
Now that you know the horizontal and vertical components of motion you could answer questions such as
bull How long will the ball be in the airbull How high with ball getbull How far away from the spot it was
hit will it land
Since we know the total time of flight and the velocity of the ball in the horizontal direction we can use the following formula
Δx = vt V = 26ms t =3s
x = 78m
300ms
30deg
150msVy
260msVx
A golf ball is hit eastward at an angle of 30deg with respect to the ground with an initial velocity of
300ms What are are the horizontal and vertical components of the golf ballrsquos motion
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Determine the ComponentsFor each image below determine the x and y components using trig
250m
40deg
Y-component
X-component
[1]22
ms
67deg
Y-component
X-component
[2]
250m40deg
Y-component
X-component
[3]
250m
30deg
Y-component
X-component
[4]
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Adding and Subtracting Vectors
bull It takes longer to fly to California than it does to fly back Whybull Wind usually moves from West to East Across the United States (think
about where most of our storms come from)bull When you fly West you are usually flying into the windbull When you fly East the wind is at your back pushing you
Img via physicsclassroom Img via physicsclassroom
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)Think of vector addition in terms of tug of war or pushing and pulling a box
10N10N
Net force = 0
10N5N
Net force = 5N to the right
10N
5NNet force = 15N to the right
10N
5N
Net force = 7N to the right
8N
3N7N
4N=+
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Two people are pulling a box as depicted in the image on the left Find the Resultant
The red vector is in component form and is fine We need to determine the components of the other vector fist
10N
45degY component
x component
= 7N
= 7N
So now we have 3 component vectors
10N
7N 7N
Add the red vectors
17N
7N
Use tail to tip for resultant
7N
17N
Use trig to get the magnitude and angle
Tan-1 = 7N17N = 22deg Sin(22deg)= 7NH H=19N
19N
22deg
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
5N5N
45deg
Find the Resultant 5N
45deg
Y component
x component
Resultant
45deg
5N
45deg
Y component
x component
Y = 35N northX = 35N west
Y = 35N northX = 35N eastOur Four Components
35N 35N
35N 35N
+ = 7N
The end result is that the box moves as if one force is pulling it to the North with a force of 7N
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Rules for adding and subtracting vectors1) Vectors must be parallel or in the same line to directly add or subtract them2) If not you must break a vector into components first3) Then you add and subtract vector components4) Then you get the resultant of those components (tail to tip)
10N
10N
45deg
Find the resultant
10N 10N
45deg45deg
8N
40deg
Find the resultant
9N
Find the resultant
8N
40deg40deg
8N
7N5N
3N
Find the resultant
[1]
[2]
[3]
[4]
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
NASA
A EC DB
600ms 700ms 600ms400ms800ms 400ms
1 List all the asteroids that are moving towards the ship
2 List all the asteroids that are moving away from the ship
3 Explain your reasoning
You have 5 asteroids all moving in the same direction as a rocket ship with the speeds listed below
Modified from TIPERs
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Vt = 24ms Vt = 30ms
Vt = 20ms Vt = 16ms
Vp = 8ms Vp = 10ms
Vp = 12ms Vp = 4ms
or
1 2 3 4 All the same
All Zero Cannot Determine
Greatest Least
A B
C D
Rank the velocity of the runners from the perspective of an outside observer standing besides the tracks Explain
Four cases where a person is running on a flatbed train In cases C
and D the person is running in the same
direction as the train In cases A and B the person is running in a direction opposite of the trainrsquos motion An observer is
standing outside the tracks watching
Modified from TIPERs
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Ntipers Vector Question2-SCT08 ADDING TWO VECTORSmdashMAGNITUDE OF THE RESULTANT 111308811130881113088 Three students are discussing the magnitude of t he resultant of the addition of the vectors A and B Vector A has a 1113088 magnitude of 5 cm and vector B has a magnitude of 3 cm
Alexis ldquoWersquod have to know the directions of the vectors to know how big the resultant is going to berdquo Bert ldquoSince we are only asked about the magnitude we donrsquo t have to worry about the directions The magnitude is just the size so to find the magnitude of the resultant we just have to add the sizes of the vectors The magnitude of the resultant in this case is 8 cmrdquo Cara ldquoNo these are vectors and to find the magnitude you have to use the Pythagorean theorem In this case the magnitude is the square root of 34 a little less than 6 cmrdquo Dacia ldquoThe resultant is the vector that you have to add to the first vector to get the second vector In this case the resultant is 2rdquo
With which if any of these students do you agree Alexis _____ Bert _____ Cara _____ Dacia_____ None of them_____
Explain your reasoning
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
(a) List all the velocities that have a zero x-component (b) List all the velocities that have a zero y-component(c) List all the velocities that have an x-component pointing in the positive x-direction (d) List all the velocities that have a y-component pointing in the negative y-direction
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Compressed String
If you simultaneously drop an object and shoot an object horizontally from the same height which one hits the ground first
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
0 s
1 s
2 s
3 s
DroppedThrown
They hit at the same time The vertical component of motion has nothing to do with how fast an object falls The only acceleration in that scenario is gravity and it acts exclusively in the y direction
4 s
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
RangeAssumptionsbull Earth is flatbull Uniform gravitational fieldbull No air resistancebull Launch height = landing height
If you know initial velocity and the angle of launch the range formula simplifies finding horizontal displacement assuming the following conditions are true
1 A golf ball is driven off of a tee with an initial velocity of 70ms at an angle of 12deg with respect to the ground How far does it go
2 A football is kicked with an initial velocity of 23 ms at an angle of 43deg with respect to the ground how far away will it land
3 A long jumper has an initial velocity of 11 ms at an angle of 26deg How far can he jump
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
bull Range and Max Height
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Img via httpsshareehsuenorg
A ramp is elevated so that a ball rolls down it without slipping and then off of a table Just upon reaching the bottom of the ramp the ball has a horizontal velocity of 5ms You need to calculate where it will land and then place a cup in that spot Then we will test your calculations
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Img via httpsshareehsuenorg
Angle of the Ramp
Horizontal Velocity
Average Vx
20deg
30deg
40deg
50deg
Horizontal Displacement Δx = Vixt
Vertical Free Fall TimeΔy = Viyt + frac12at2
Calculate the horizontal velocity of a projectile that rolls down an inclined plane with our different elevations Conduct 5 trials for each angle and get an average value Make sure you redo any ldquooutliersrdquo
Create a graph of elevation angle vs horizontal velocity Is it linear Can you infer anything about the angle of an inclined plane and acceleration
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Img via httpsshareehsuenorg
A ball rolls down a 1m down a ramp elevated at 45deg without slipping and then falls off a 1m high table Where it will land
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
Bullet Drop in Battlefield vs CoD
bull None in CoDbull Battlefield is not necessary more accuratebull Sure they have bullet drop but they often inflate it
due to small map sizesbull Game files show g as being 15ms2
bull Why When playing TDM type games the maps are so small and the guns so powerful and have such a high muzzle velocity that the bullet drop has to be exaggerated to be relevant
- Slide 1
- Imagine trying to swim directly across a river that has a curre
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Breaking a Vector into Components
- Breaking a Vector into Components (2)
- Breaking a Vector into Components (3)
- Breaking a Vector into Components (4)
- Breaking a Vector into Components (5)
- Slide 33
- Adding and Subtracting Vectors
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Ntipers Vector Question
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Range
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Bullet Drop in Battlefield vs CoD
-
