Motion in Two Dimensions Unit Student Success Sheets...

---Motion in two dimensions sss ---

Motion in Two Dimensions Unit Student Success Sheets (SSS)

Civic Memorial High School - Physics

Concept # What we will be learning Mandatory Practice

1 Vectors Practice problems 1

2 Relative Motion Practice problems 2

3 Free Fall Practice problems 3

4 Projectile Motion Practice problems 4

5 Velocity of Projectiles Practice problems 5

6 Projectile Angles Practice problems 6

7 Range and Air Resistance Practice problems 7

Modified by Mrs. Ward with permission from Crystal Kirch at flippingwithkirch.blogspot.com

http://flippingwithkirch.blogspot.com/


Concept 1 Concept 2 Concept 3

Concept 4 Concept 5 Concept 6

Concept 7




#1 Vectors

Recall that an __________ number in Physics is referred to as __________. Many times in Physics a __________ is not enough. You also need a __________. A vector is a __________ that has both a length and __________. The __________ of a vector is referred to as its __________. We draw vectors by using __________. A __________ is made up by __________. To __________ a vector means to find its components; a vector’s components are the __________ of the vector along __________ __________. __________ for a vector’s components is actually very _____ and requires only a little _____________. You must break it down into it’s __ and __ components. Using those x and y components you can form a _______ triangle.




____ and ____ are used to solve for x and y components. Tan is used if you have the __________ but need the __________. Sometimes you also need the equation a2 + b2 = c2 to find the __________ of any of the three _____. Quick Example: At a local ski resort you take a rope tow to the top of the bunny slope. Your displacement vector for this trip has a length of 190 m and points at an angle of 26o above the horizontal. During the ride to the top, how far have you gone in (a) the horizontal direction and (b) the vertical direction? Practice problems 1: Find the x and y components of a position vector that has a magnitude of r = 75.0 m and an angle relative to the x axis of (a) 35.0o and (b) 65.0o. The press box at a baseball park is 9.75 m above the ground. A reporter in the press box looks at an angle of 15.0o below the horizontal to see second base. What is the horizontal distance from the press box to second base?




#2 Relative motion

Relative motion means the motion of one object __________ to another _______. For example if someone is walking 1.2 m/s on a train going 7.0 m/s then their motion relative to the ground is 8.2 m/s. If the person was walking to the ______ of the train with the same velocity then the relative motion would be ________. Quick example: A worker of a train climbs a ladder with a speed of Vy = 0.20 m/s, as a train coasts forward at vx = 0.70 m/s. Find the speed and the direction of the worker relative to the ground. Practice Problems 2: The pilot of an airplane wants to fly due north, but there is a 65 km/hr wind blowing from east to west. in what direction should the pilot head her plane if its speed relative to the air is 340 km/hr? give your answer in degrees north of east. A ferry approaches shore, moving north with a speed of 6.2 m/s relative to the dock. A person on the ferry walks from one side of the ferry to the other, moving east with a speed of 1.1 m/s relative to the ferry. What is the speed of the person relative to the dock? A person on a cruise ship is doing laps on the promenade deck. On one portion of the track the person is moving north with a speed of 3.8 m/s relative to the ship. The ship moves east with a speed



---Motion in two dimensions sss --- of 12 m/s relative to the water. What is the direction of motion of the person relative to the water?

#3 Free Fall

Galileo _______ dropped objects from the leaning tower of Pisa to study _____ _____. Galileo concluded that if the effects of air __________ can be __________ then all objects in free fall have the ______ constant __________. Galileo’s conclusion applies to ___ objects,__________ of size or weight. Air resistance must be _____ enough to __________. This theory was __________ with an experiment carried out on the ______ where they dropped a __________ and a __________ Free fall does not __________ mean the object is moving __________. If you toss something in the air it is in free fall on the way ___ and ______. It’s __________ is constant the entire time until it hits the ______. The __________ is due to __________. The __________ produced by __________ at Earth’s __________ is denoted with a g or ag.



---Motion in two dimensions sss --- For all of our calculations g = 9.81 m/s2. The __________ of motion determines if it is 9.81 m/s2 or -9.81 m/s2. The __________ of an object changes ______ than the velocity each passing _______. Distance __________ with time squared (t2). This is referred to as a __________ relationship. The __________ of an object in free fall __________ by the same amount with each passing __________. Velocity increases __________ with time (t). This is referred to as a __________ relationship. Quick Example: A boy steps off the end of a 3.00 m high diving board and drops to the water below. (a) How much time does it take for him to reach the water? (b) What is the boy’s speed on entering the water? Practice problems 3: seagulls are often observed dropping clams and other shellfish from a height onto rocks below, as a means of opening the shells. if a seagull drops a shell from rest from a height of 14 m, how fast is the shell moving when it hits the rocks? A volcano launches a lava bomb straight upward with an initial speed of 28 m/s. Taking upward to be the positive direction, find the speed and direction of motion of the lava bomb (a) 2.0 s and (b) 3.0 s after it is launched.




#4 Projectile Motion

__________ are objects that are launched or __________ into the air. Air resistance can be __________. Acceleration due to __________ is constant in the ______ direction at g = 9.81 m/s2. Air resistance being __________ is in an ______ situation. In cases where air resistance is __________ projectiles _______ from ideal behavior. Air resistance causes __________ which ______ down projectiles and reduces the distance __________. __________ and __________ motion are independent of each other. The ____ of flight depends only on __________ speed. The__________ distance of travel is the __________ speed times the ______ of flight. We start with the position-time equation from last unit.

Xf = Xi + Vit + 1/2at2

Since projectiles have two ranges of motion we have to apply this in the x and y direction.

Xf = Xi + Vxit + ½ axt2




Yf = Yi + Vyit + ½ ayt2 A projectile experiences a __________ acceleration due to __________. There is ___ acceleration in the x direction. This means ax = 0 and ay = -g

quick example: A person skateboarding with a constant speed of 1.30 m/s releases a ball from a height of 1.25 m above the ground. Given that xi = 0 and yi = 1.25 m, find xf and yf for the times (a) t = 0.250 s and (b) t = 0.500 s. recall that g = 9.81 m/s2. practice problems 4: A soccer ball is kicked from the ground with an initial speed of 12 m/s at an angle of 32o above the horizontal. What are the x and y positions of the ball 0.50 s after it is kicked?

playing shortstop, you pick up a ground ball and throw it to second base. the ball is thrown horizontally, with a speed of 22 m/s, directly toward point A. when the ball reaches the second baseman 0.45 s later, it is caught at point b. (a) how far were you from the second baseman? (b) what is the distance of the vertical drop from point A to point b?




#5 Velocity of Projectiles

The __________ position of the projectile __________ steadily with time. The __________ position changes by an __________ amount with each time _________. The vertical motion is the _______ as the free fall of an object dropped from _______. An ______ projectile follows a __________ path __________ of how it is launched. You already learned the velocity time equation: Vf = Vi + at We apply this equation in x and y just as before.

Vxf = Vxi + axt Vyf = Vyi + ayt For a projectile we know ax = 0 and ay = -g

quick example: you throw a baseball from the roof of a house to a friend on the ground. the ball has an initial velocity of 12.0 m/s in the horizontal direction. after 1.00 s, how fast is the ball moving in (a) the x direction and (b) the y direction?



---Motion in two dimensions sss --- practice problems 5:

A crow is flying horizontally with a constant speed of of 2.70 m/s when it releases a clam from its beak. the clam lands on a rocky beach 2.10 s later. just before the clam lands, what is, (a) its horizontal component of velocity and (b) its vertical component of velocity? a snowball is thrown with an initial x velocity of 7.5 m/s and an initial y velocity of 8.2 m/s. how much time is required for the snowball to reach the highest point? (hint: the highest point of a projectile corresponds to the time when Vyf = 0.)

#6 Projectile Angles

Projectiles ________ always start off in the __________ direction. Projectiles can be __________ in any __________ and at any __________. _______ can be used to find the _______ or velocity.

Vxi = Vi cosΘ Vyi = Vi sinΘ We substitute our velocity equations into our Position-Time equations and velocity time equations.



---Motion in two dimensions sss --- quick example: chipping from the rough, a golfer sends the ball over a 3.00 m high tree that is 14.0 m away. the ball lands on the green, of course, at the same level at which it was struck, after traveling a horizontal distance of 17.8 m. (a) if the ball left the club at an angle of 54.00 above the horizontal and landed on the green 2.24 s later, what was the initial speed? (b) the ball passes directly over the tree at t=1.76 s. how high was the ball at that time?

practice problems 6: what is the speed of the golf ball in the quick example when it passes over a tree? A soccer ball is kicked from the ground with an initial speed of 12 m/s at an angle of 32o above the horizontal. what are the x and y positions of the ball 0.50 s after it is kicked? In the problem above what are the x and y components of the soccer ball’s velocity 0.50 s after it is kicked?




#7 range and Air resistance

How far can you throw a football? The answer depends on the __________ and __________ you threw it at. The __________ of a projectile is the horizontal distance it travels before ________.

__________ range occurs when the launch angle is Θ = 45o Air resistance or other forms of __________ do not act on _______ projectiles. _______ everyday projectiles are good ______________ to the ideal case. When a __________ amount of air resistance is applied the range is __________. Practice problems 7: The hang time of a punt is measured to be 4.50 s. if the ball was kicked at an angle of 63.0o above the horizontal and was caught at the same level from which it was kicked, what was its initial speed?



---Motion in two dimensions sss --- A soccer ball is kicked from ground level. how much time does it take for the ball to return to the ground if it is kicked with an initial speed of 14 m/s at an angle of 53o above the horizontal?



Motion in Two Dimensions Unit Student Success Sheets...

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