An autographed baseball rolls off

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 1

This print-out should have 52 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering.

001 2.0 points At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant. What is the speed of the pilot relative to

the ground?

1. √

v2 1 + v2

2

2. v2 − v1

3. √

v2 1 − v2

2

4. v1 + v2

5. v1 − v2

002 (part 1 of 2) 2.0 points A particle travels to the right at a constant rate of 6.2 m/s. It suddenly is given a vertical acceleration of 2.3 m/s2 for 4 s. What is its direction of travel after the

acceleration with respect to the horizontal? Answer between −180◦ and +180◦. Answer in units of ◦

003 (part 2 of 2) 2.0 points What is the speed at this time? Answer in units of m/s

004 2.0 points A particle moving at a velocity of 8.9 m/s in the positive x direction is given an accelera- tion of 5.9 m/s2 in the positive y direction for 3.7 s. What is the final speed of the particle? Answer in units of m/s

005 (part 1 of 3) 2.0 points

A particle moves in the xy plane with constant acceleration. At time zero, the particle is at x = 2 m, y = 6.5 m, and has velocity ~vo = (2.5 m/s) ı̂ + (−8.5 m/s) ̂ . The acceleration is given by ~a = (3.5 m/s2) ı̂+ (5 m/s2) ̂ . What is the x component of velocity after

1.5 s? Answer in units of m/s

006 (part 2 of 3) 2.0 points What is the y component of velocity after 1.5 s? Answer in units of m/s

007 (part 3 of 3) 2.0 points What is the magnitude of the displacement from the origin (x = 0 m, y = 0 m) after 1.5 s? Answer in units of m

008 (part 1 of 3) 2.0 points

A ball is thrown and follows the parabolic path shown. Point Q is the highest point on the path and points P and R are the same height above the ground.

Q

RP

How do the speeds of the ball at the three points compare? Air friction is negligible.

1. ‖~v Q ‖ < ‖~v

P ‖ = ‖~v

R ‖

2. ‖~v P ‖ < ‖~v

Q ‖ < ‖~v

R ‖

3. ‖~v P ‖ = ‖~v

R ‖ < ‖~v

Q ‖

4. ‖~v Q ‖ < ‖~v

R ‖ < ‖~v

P ‖

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 2

5. ‖~v R ‖ < ‖~v

Q ‖ < ‖~v

P ‖

009 (part 2 of 3) 2.0 points Which diagram best indicates the direction of the acceleration, if any, on the ball at point R?

1.

2.

3.

4.

5.

6.

7.

8. The ball is in free fall and there is no acceleration at any point on its path.

9.

010 (part 3 of 3) 2.0 points Which diagram best indicates the direction of the net force, if any, on the ball at point Q?

1.

2.

3.

4.

5.

6. The ball is in free-fall and there is no acceleration at any point on its path.

7.

8.

9.

011 (part 1 of 3) 2.0 points A ball of mass 0.4 kg, initially at rest, is kicked directly toward a fence from a point 20 m away, as shown below. The velocity of the ball as it leaves the

kicker’s foot is 17 m/s at angle of 39 ◦ above the horizontal. The top of the fence is 4 m high. The ball hits nothing while in flight and air resistance is negligible. The acceleration due to gravity is 9.8 m/s2.

b

20 m

4 m

17 m /s

39 ◦

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

b

Determine the time it takes for the ball to reach the plane of the fence. Answer in units of s

012 (part 2 of 3) 2.0 points How far above the top of fence will the ball

pass? Consider the diameter of the ball to be negligible.

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 3

Answer in units of m

013 (part 3 of 3) 2.0 points What is the vertical component of the velocity when the ball reaches the plane of the fence? Answer in units of m/s

014 2.0 points The velocity of a projectile at launch has a horizontal component vh and a vertical com- ponent vv. When the projectile is at the high- est point of its trajectory, identify the vertical and the horizontal components of its velocity and the vertical component of its acceleration. Consider air resistance to be negligible.

Vertical Horizontal Vertical Velocity Velocity Acceleration

1. vv 0 0

2. 0 vh 0

3. vv vh 0

4. 0 0 g

5. 0 vh g

015 2.0 points

A ball is thrown and follows the parabolic path shown. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground.

Q

RP

How do the speeds of the ball at the three points compare?

1. ‖~v Q ‖ < ‖~v

R ‖ < ‖~v

P ‖

2. ‖~v R ‖ < ‖~v

Q ‖ < ‖~v

P ‖

3. ‖~v Q ‖ < ‖~v

P ‖ = ‖~v

R ‖

4. ‖~v P ‖ < ‖~v

Q ‖ < ‖~v

R ‖

5. ‖~v P ‖ = ‖~v

R ‖ < ‖~v

Q ‖

6. ‖~v P ‖ = ‖~v

R ‖ = ‖~v

Q ‖

016 2.0 points

A ball is thrown and follows the parabolic path shown. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground.

Q

RP

Which of the following diagrams best indi- cates the direction of the acceleration, if any, on the ball at point P?

1.

2. The ball is in free-fall and there is no acceleration at any point on its path.

3.

4.

5.

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 4

6.

7.

8.

9.

017 2.0 points

A ball is thrown and follows the parabolic path shown. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground.

Q

RP

Which of the following diagrams best indi- cates the direction of the acceleration, if any, on the ball at point R?

1.

2.

3.

4.

5.

6.

7.

8. The ball is in free-fall and there is no acceleration at any point on its path.

9.

018 2.0 points

A bowling ball accidentally falls out of the cargo bay of an airliner as it flies along in a horizontal direction.

Z

Y

X

W

U

V

As observed by a person standing on the ground and viewing the plane as in the fig- ure, which path would the bowling ball most closely follow after leaving the airplane?

1. X

2. Y

3. V

4. U

5. Z

6. W

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 5

019 2.0 points Aman can throw a ball a maximum horizontal distance of 169 m on a level field. The acceleration of gravity is 9.8 m/s2 . How far can he throw the same ball verti-

cally upward from the ground? (Assume that the ball is thrown from the ground and that his muscles give the ball the same speed in each case.) Answer in units of m

020 2.0 points Assume: A 78 g basketball is launched at an angle of 40.4◦ and a distance of 17.8 m from the basketball goal. The ball is released at the same height (ten feet) as the basketball goal’s height. A basketball player tries to make a long

jump-shot as described above. The acceleration of gravity is 9.8 m/s2 . What speed must the player give the ball? Answer in units of m/s

021 (part 1 of 3) 2.0 points A cannon sends a projectile towards a target a distance 1490 m away. The initial velocity makes an angle 39◦ with the horizontal. The target is hit. The acceleration of gravity is 9.8 m/s2 . What is the magnitude of the initial veloc-

ity? Answer in units of m/s

022 (part 2 of 3) 2.0 points How high is the highest point of the trajec- tory? Answer in units of m

023 (part 3 of 3) 2.0 points How long does it take for the projectile to reach the target? (Assume no friction) Answer in units of s

024 2.0 points If you are standing in a bus that moves at constant velocity and drop a ball from your outstretched hand, you will see its path as a vertical straight line.

How will the path appear to a friend stand- ing at the side of the road?

1. The path is a straight line slanted down.

2. The path is a straight line orientated vertically.

3. The path curves downward.

4. The path curves upward.

025 (part 1 of 2) 2.0 points A person can jump a horizontal distance of 2.55 m on the Earth. The acceleration of gravity is 5.91 m/s2 . How far could he jump on the Moon, where

the free-fall acceleration is 0.297g? Answer in units of m

026 (part 2 of 2) 2.0 points Repeat for Mars, where the acceleration due to gravity is 0.206g . Answer in units of m

027 2.0 points Two bodies are falling with negligible air resis- tance, side by side, above a horizontal plane. If one of the bodies is given an additional

horizontal acceleration during its descent, it

1. follows a straight line path along the re- sultant acceleration vector.

2. follows a hyperbolic path.

3. strikes the plane at the same time as the other body.

4. has the vertical component of its velocity altered.

5. has the vertical component of its acceler- ation altered.

028 2.0 points Immediately after being fired from a cannon, a high-speed cannonball does not possess

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 6

1. It possesses all of these.

2. both mass and momentum.

3. momentum.

4. force.

5. both force and kinetic energy.

6. mass.

7. both force and momentum.

8. both momentum and kinetic energy.

9. both mass and force.

10. kinetic energy.

029 2.0 points At what point in its trajectory does a batted baseball have its minimum speed?

1. at the beginning point

2. at the top

3. somewhere at the middle height

4. at the end point

030 2.0 points An autographed baseball rolls off of a 0.99 m high desk and strikes the floor 0.80 m away from the desk. How fast was it rolling on the desk before

it fell off? The acceleration of gravity is 9.81 m/s2 . Answer in units of m/s

031 2.0 points A football is thrown toward a receiver with an initial speed of 16.5 m/s at an angle of 38.7◦ above the horizontal. At that instant, the receiver is 16.2 m from the quarterback. The acceleration of gravity is 9.81 m/s2 . With what constant speed should the re-

ceiver run to catch the football at the level at

which it was thrown? Answer in units of m/s

032 2.0 points A bullet fired horizontally hits the ground in 0.5 sec. If it had been fired with a much higher

speed in the same direction, and neglecting air resistance and the earth’s curvature, it would have hit the ground in

1. less than 0.5 sec.

2. 0.5 sec.

3. There is no way to tell from the informa- tion given.

4. more than 0.5 sec.

033 (part 1 of 4) 2.0 points A ball is thrown horizontally from the top of a building 42.7 m high. The ball strikes the ground at a point 41.9 m from the base of the building. The acceleration of gravity is 9.8 m/s2 . Find the time the ball is in motion. Answer in units of s

034 (part 2 of 4) 2.0 points Find the initial velocity of the ball. Answer in units of m/s

035 (part 3 of 4) 2.0 points Find the x component of its velocity just be- fore it strikes the ground. Answer in units of m/s

036 (part 4 of 4) 2.0 points Find the y component of its velocity just be- fore it strikes the ground. Answer in units of m/s

037 2.0 points

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 7

038 (part 1 of 2) 2.0 points A projectile is fired straight upward at 118 m/s. How fast is it moving at the instant it

reaches the top of its trajectory? Answer in units of m/s

039 (part 2 of 2) 2.0 points How fast is it moving at the instant it reaches the top of its trajectory if the projectile is fired upward at 41◦ from the horizontal? Answer in units of m/s

040 2.0 points A football is thrown at an angle of 37◦ above the horizontal. Assume the ball is throw and received at the same height. To throw a 52.1 m pass, what must be the

initial speed of the ball? The acceleration due to gravity is 9.8 m/s2 . Answer in units of m/s

041 (part 1 of 3) 2.0 points

A student stands at the edge of a cliff and throws a stone horizontally over the edge with

a speed of 16.9 m/s. The cliff is 23.9 m above a flat, horizontal beach.

x

y

2 3 .9

m

16.9 m/s

g

O

How long after being released does the stone strike the beach below the cliff? The acceler- ation of gravity is 9.8 m/s2 . Answer in units of s

042 (part 2 of 3) 2.0 points At impact, what is its speed? Answer in units of m/s

043 (part 3 of 3) 2.0 points At what angle below the horizontal does it land? Answer in units of ◦

044 (part 1 of 2) 2.0 points An arrow is shot at an angle 39 ◦ with the horizontal. It has a velocity of 52 m/s. How high will the arrow go? The accelera-

tion of gravity is 9.8 m/s2 . Answer in units of m

045 (part 2 of 2) 2.0 points What horizontal distance will it travel? Answer in units of m

046 (part 1 of 2) 2.0 points In a local bar, a customer slides an empty beer mug on the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor d = 2.16 m from the base of the counter. The height of the counter is h = 1.3 m.

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 8

The acceleration of gravity is 9.8 m/s2 . How long after sliding off the edge of the

counter does the mug hit the floor?

1. t = 2 d√ h g

2. t = 2h√ d g

3. t =

√

g

d

4. t = d g

5. t =

√

2 d

g

6. t =

√

2 (d+ h)

g

7. t =

√

2h

g

8. t =

√

g

h

9. t = d

2 g

10. t = √

h g

047 (part 2 of 2) 2.0 points With what speed did the mug leave the counter? Answer in units of m/s

048 2.0 points When you throw an object horizontally off

the side of a cliff, it follows a path similar to the one below.

v0 y

x

Which statement is false if air resistance is negligible?

1. The y-component of the object’s velocity ~v varies with time.

2. The x-component of the object’s velocity ~v varies with time.

3. The acceleration of the object is a con- stant vector, independent of time.

4. The position vector ~r, which locates the object relative to the origin of coordinates, varies with time.

049 2.0 points A ball is thrown horizontally at speed v0

from the top edge of a cliff of height h. Neglecting air resistance, which statement

is wrong?

1. The time it takes for the ball to hit the ground depends on v0, g and h.

2. The time it takes for the ball to hit the ground does not depend in any way on v0.

3. The ball is freely falling with acceleration ~g, from the instant it is released until it strikes the ground.

4. The horizontal distance traveled from the base of the cliff to the spot where the ball hits the ground depends on v0 .

050 2.0 points Two little boys of the same height stand on a fairly high terrace. Each has a ball, and each throws the ball at the same angle and same speed, but one boy (P) throws the ball at θ0 above the horizontal, while the other boy (Q) throws the ball at θ0 below the horizontal. Everything else is the same. How do the speeds with which the two balls

hit the ground compare? Specifically, what is vP vQ

?

rouzbehani (mr39949) – Motion in 2D – bump – (1004) 9

1. vP vQ

> 1.

2. vP vQ

< 1.

3. Not enough information is given.

4. vP vQ

= 1 (the same final speed)

051 (part 1 of 2) 2.0 points You drop a stone from a position of rest. How far will it fall vertically in the first 3 s?

The acceleration of gravity is 9.8 m/s2 . Answer in units of m

052 (part 2 of 2) 2.0 points If you instead toss it horizontally at 3.8 m/s, how far will it fall vertically in the first 3 s?