Projectile Motion - Fulmer's Physics · Projectile Motion Horizontal component- when no horizontal...
Transcript of Projectile Motion - Fulmer's Physics · Projectile Motion Horizontal component- when no horizontal...
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Projectile Motion
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Vector QuantitiesA quantity such as force, that has
both magnitude and direction.
Examples: Velocity, Acceleration
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Scalar QuantitiesA quantity such as mass, volume, and
time, which can be completely specified by it’s magnitude, and has
no direction.
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Vector A quantity that has magnitude and
direction Usually represented by an arrow whose
length represents the magnitude and direction represents the direction
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Vector scaled 1 cm = 20 m/s
This vector represents 60 m/s to the right.
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Resultant The vector sum of the two or
more component vectors
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3 Step Technique1) Draw the two vectors with their tails
touching
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2) Draw a parallel projection of each vector with dashed lines to form a rectangle.
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3) Draw the diagonal from the point where the two tails are touching.
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OR 1. Connect Draw the first vector
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OR 1. Connect Draw the first vector 2. Connect the tail of the second to the
head of the first
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OR 1. Connect Draw the first vector 2. Connect the tail of the second to the
head of the first 3. Draw the Diagonal
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Sample QuestionIf a plane heads north at 100m/s and the wind is traveling south at 20m/s.
What is the resulting velocity?
100 m/s
20 m/s
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Finding the magnitude of the sides 1.Use the Pythagorean Theorem 2.(7-m)2 + (9-m)2 = c2 3.130-m2 = c2 4. 11.4-m = c
7-m
9-m
11.4-m
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VectorsThe 3-unit and 4-unit vectors add to
produce a resultant vector of 5 units, at 37.5 degrees from the
horizontal
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VectorsThe diagonal of a square is 2, times the length of one of its sides.
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Hansel and Gretel walked straight north for 6-km from their home and then headed east for 12- km. What is their displacement from home?
13.4-km They then walked south for 20-km. What is their current displacement from home?
18.4-km
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Components of VectorsResolution- the process of
solving a vector into components
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Components of VectorsAny vector drawn can be resolved
into vertical and horizontal components
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Finding the Angle from the OriginWhen dealing with right triangles there are 3 trigonometric functions SOH- Sine= Opposite/Hypotenuse CAH- Cosine= Adjacent/Hypotenuse TOA- Tangent= Opposite/Adjacent
Opposite Hypotenuse
Adjacent Angle Trying to find
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Find Angle using Tangent
12 (Opposite)
5 (Adjacent)
Angle θtan(θ) = 12/5
tan(θ) = 2.4
θ = tan-1(2.4)
Tangent= Opposite/Adjacent
How is this done on our calculators?
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Calculator 1.Make sure calculator is in DEGREES
2.2nd function
3. DRG
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Calculator 1.Find Inverse Tangent of 2.4 2.2nd function 3. tan-1
4.Enter 2.4 5.Press = 6. 67.4º
32.82.4
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A Football field has a total length off 120-meters and is 50 –meters wide. What is the length of the diagonal? What angle does it make if the end-zone is the base?
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Suppose that a river was moving with a velocity of 3 m/s N and the boat was moving at 4 m/s E. What would be the resultant speed (m/s)?
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Suppose that a river was moving with a velocity of 3 m/s N and the boat was moving at 4 m/s E. What would be the resultant angle of the boat?
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Hansel and Gretel walked straight north for 6-km from their home and then headed east for 12- km. What is their angle or direction from home?
63o East of North
They then walked south for 20 miles. What is their current angle or direction from home?
49o South of East or 139o
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Projectile MotionProjectile- any object that moves
through air or through space, acted on only by gravity
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Projectile MotionProjectiles near the surface of the
Earth follow a curved path, due to the force of gravity.
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Projectile MotionHorizontal component- when no
horizontal force acts on a projectile, horizontal velocity is constant
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Sample Question
At the instant a horizontally pointed cannon is fired, a cannonball held at the
canon’s side is released and drops to the ground. Which cannonball strikes the ground first, the one fired from the
cannon or the one dropped?
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ProjectilesThe path traced by a projectile accelerating only in the Vertical
direction while moving at a constant horizontal velocity is a parabola.
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Air ResistanceWhen air resistance is small enough to neglect, usually for slow moving or very heavy projectiles, the curved paths are parabolic. Air Resistance is TOO complex for our Introduction to Physics Class
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Projectile MotionVertical component- response to the force of gravity
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Projectile MotionIMPORTANT:
The horizontal component of motion for a projectile is completely independent of the vertical component of
motion.
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Upwardly Launched Projectiles
With no gravity, the projectile will follow a straight-line
path.
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Upwardly Launched Projectiles
● The horizontal range of a projectile depends on the angle of launched.
● The greater the launch angle, the higher the projectile will go, but…
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Upwardly Launched Projectiles
Complimentary launch angles will travel the same horizontal distance!!!
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For a projectile, the only force acting upon it is:
A) MOMENTUM B) FORCE C) GRAVITY D) INERTIA
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A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical and horizontal acceleration?
A) V: 10 m/s2 up, H: 0 m/s2 B) V: 0 m/s2 up, H: 10 m/s2 C) V: 10 m/s2 down, H: 0 m/s2 D) V: 10 m/s2 down, H: 10 m/s2
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At what point in its path does a projectile have minimum speed?
A)at the beginning B) at the top C) when it is about to land
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In the absence of gravity, any launched projectile will travel what type of path?
A) parabolic B) straight C) vertical D) horizonal
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At the instant a horizontally pointed cannon is fired, a cannonball held at the canon’s side is released and drops to the ground. Which cannonball strikes the ground first, the one fired from the cannon or the one dropped?A) The one from the cannon B) The one dropped C) Both hit the ground at the same time D) Neither, they fly randomly off into
Psychology class
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Calculations for Cliff1. Find the time to hit the ground.
a. Measure height (y) b. Use y = ½ atv
2 or [tv = (2y/a)1/2]
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Calculations for Cliff1. Find the time to hit the ground.
a. Measure height (y) b. Use y = ½ atv
2 or [tv = (2y/a)1/2]
2. Find the horizontal velocity (vh) a. Find the time (th) to go horizontal (x)
b. vh = x/th
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Calculations for Cliff1. Find the time to hit the ground.
a. Measure height (y) b. Use y = ½ atv
2 or [tv = (2y/a)1/2]
2. Find the horizontal velocity (vh) a. Find the time (th) to go horizontal (x)
b. vh = x/th
3. Find horizontal distance traveled from base of cliff a. Distance = vh tv
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A student standing on the roof of a 50.0-meter-high building kicks a stone at a horizontal speed of 4.00 meters per second. How much time will it take the stone to hit the ground?
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A student standing on the roof of a 50.0-meter-high building kicks a stone at a horizontal speed of 4.00 meters per second. How far from the base of the building will the stone hit?
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Calculations for LaunchGiven the initial Velocity vi and Angle θ A. Find Components of Velocity 1. vv = vi sin θ 2. vh = vi cos θ
vv
vh
vi
θ
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Calculations for LaunchGiven the initial Velocity vi and Angle θ A. Find Components of Velocity 1. vv = vi sin θ 2. vh = vi cos θ
B. Find time to get to top of path (B) 1. a = (vB - vA)/t 2. vB = 0 3. t = - vA/a
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Calculations for LaunchGiven the initial Velocity vi and Angle θ A. Find Components of Velocity B. Find time to get to top of path (B) 1. vv = vi sin θ 1. a = (vTOP - vv)/t 2. vh = vi cos θ 2. vTOP = 0 3. t = - vv/a
C. Height y = ½ at2
D. Total distance travelled x = vh(2t)
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An athlete kicks a ball at a 30o angle at 56 m/s. What is the vertical velocity in m/s? 56 m/s sin (30o) = 28 m/s What is the horizontal velocity in m/s? 56 m/s cos (30o) = 48 m/s
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An athlete kicks a ball at a 30o angle at 56 m/s. vv = 28 m/s vh =48 m/s
How much time until it reaches maximum height? t = (28 m/s)/(10 m/s2) = 2.8 s
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An athlete kicks a ball at a 30o angle at 56 m/s. vv = 28 m/s vh =48 m/s t = 2.8 s
How far down field does the ball land? x = 48 m/s (2 x 2.8 s) = 269 m
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Fast-Moving Projectiles
Satellite – an object that falls around the Earth or some other body rather
than into it
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SatellitesCurvature of the earth enters into
our calculations
If an object is moving at 8000 m/sec AND it starts falling from 5 m above the surface It will be 5 m above the ground after 1-s
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SatellitesThrow at 8000 m/sec This is about 18,000 mph Earth circumference is 25,000 miles Takes 25000/18000 = 1.4 hours = 84 minutes Higher altitude longer
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Satellites
Force of gravity on bowling ball is at 90o to velocity, so it doesn’t
change the velocity!!!
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If no air resistance, gravity doesn’t
change speed of satellite, only
direction!!!
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WHAT DO WE CALL A PROJECTILE THAT CONTINUALLY
FALLS AROUND EARTH?
A) A ROTATING PROJECTILE
B) A SATELLITE
C) AN ORBITING OBJECT
D) A PLANET
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What will happen if a satellite is launched with more velocity than is needed to stay in orbit?
A) IT WILL EXIT THE EARTH’S GRAVATIONAL INFLUENCES AND CONTINUE IN MOTION WITHOUT ACUTALLY ORBITING EARTH.
B) IT WILL EXIT THE EARTH’S GRAVATIONAL INFLUENCES AND CATCH ON FIRE WHILE ORBITING THE EARTH
C) IT WILL LEAVE THE SOLAR SYSTEM AND BECOME IT’S OWN PLANET
D) THE GOVERNMENT WILL USE IT TO SPY ON OTHER COUNTRIES.