Deck 4: Two-Dimensional Kinematics

Question 1

A ball is thrown at an angle of θ above the horizontal. If there is no acceleration due to gravity the ball will follow a straight-line path.

Answer 1

True

Question 2

A projectile is launched from ground level with a certain speed. For any range less than the maximum range there are two possible launch angles that give the same range.

Answer 2

True

Question 3

Two objects are thrown vertically upwards simultaneously, one on the surface of Earth and the other on the surface of the Moon. Both have an initial velocity of 20 m/s. Both objects will take the same time to reach the highest point of their trajectory.

Answer 3

False

Question 4

For general projectile motion, the vertical component of a projectile's acceleration

A) is zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) any of the above, depending on position.

Question 5

For general projectile motion, the horizontal component of a projectile's acceleration

A) is zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) any of the above, depending on position.

Question 6

If the acceleration vector of an object is directed parallel to the velocity vector,

A) the object is turning.
B) the object is speeding up.
C) the object is slowing down.
D) the object is not moving.
E) this situation would not be physically possible.

Question 7

James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. Compare the time it takes each to reach the lake below.

A) James reaches the surface of the lake first.
B) John reaches the surface of the lake first.
C) James and John will reach the surface of the lake at the same time.
D) Cannot be determined without knowing the mass of both James and John.
E) Cannot be determined without knowing the weight of both James and John.

Question 8

If the acceleration vector of an object is directed perpendicular to the velocity vector,

A) the object is turning.
B) the object is speeding up.
C) the object is slowing down.
D) the object is not moving.
E) this situation would not be physically possible.

Question 9

James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. When they reach the lake below,

A) the splashdown speed of James is larger than that of John.
B) the splashdown speed of John is larger than that of James.
C) they will both have the same splashdown speed.
D) the splashdown speed of James will always be 9.8 m/s larger than that of John.
E) the splashdown speed of John will always be 25 m/s larger than that of John.

Question 10

For a projectile launched horizontally, the horizontal component of a projectile's velocity

A) is zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) any of the above, depending on position.

Question 11

The vertical component of the acceleration of a projectile remains constant during the entire trajectory of the projectile.

Question 12

The horizontal component of the velocity of a projectile remains constant during the entire trajectory of the projectile.

Question 13

A ball rolls off the edge of a table. The horizontal component of the ball's velocity remains constant during its entire trajectory because

A) the ball is not acted upon by any force.
B) the net force acting on the ball is zero.
C) the ball is not acted upon by a force in the horizontal direction.
D) the ball is not acted upon by a force in the vertical direction.
E) None of the other choices is correct.

Question 14

Two similar objects are thrown simultaneously from the top of a building with the same speed. One is thrown vertically downward, and the other at an angle. Both objects reach the ground at the same time.

Question 15

A mountain climber encounters a crevasse in an ice field. The opposite side of the crevasse is a height h lower, and is separated horizontally by a distance w. To cross the crevasse, the climber gets a running start and jumps in the horizontal direction. If the height of the crevasse increases but the width remains the same, then,

A) the minimum speed needed to cross the crevasse increases.
B) the minimum speed needed to cross the crevasse decreases.
C) the minimum speed needed to cross the crevasse stays the same
D) the minimum speed needed to cross the crevasse will depend on the mass of the mountain climber.
E) the minimum speed needed to cross the crevasse will depend on the weight of the mountain climber.

Question 16

For a projectile launched horizontally, the vertical component of a projectile's velocity

A) is zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) any of the above, depending on position.

Question 17

If the acceleration vector of an object is directed anti-parallel to the velocity vector,

A) the object is turning.
B) the object is speeding up.
C) the object is slowing down.
D) the object is not moving.
E) this situation would not be physically possible.

Question 18

A pilot drops a bomb from a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane will

A) be behind the bomb.
B) be over the bomb.
C) be in front of the bomb.
D) depend of the speed of the plane when the bomb was released.
E) depend of the mass of the bomb when it was released.

Question 19

For general projectile motion, the horizontal component of a projectile's velocity

A) is zero.
B) remains a non-zero constant.
C) continuously increases.
D) continuously decreases.
E) any of the above, depending on position.

Question 20

A rock is thrown at some angle above the horizontal with a certain velocity. It reaches its highest point and starts falling down. What is the velocity of the rock at the highest point of its trajectory?

A) 0
B) 9.8 m/s
C) It is equal to its initial horizontal velocity.
D) It is equal to its initial vertical velocity.
E) It is equal to its initial velocity.

Question 21

If the initial speed of a projectile is doubled.

A) Its range will be increased by 1.41.
B) Its range will double.
C) Its range will be decreased by a factor of two.
D) Its range will quadruple.
E) Its range will decrease by a factor of four.

Question 22

Marcia uses a bow to shoot an arrow with initial velocity of magnitude v₀ and at an angle θ above the horizontal. When the arrow returns to the same height from which it started,

A) the speed of the arrow is twice v₀.
B) the speed of the arrow is 9.8 times larger than v₀.
C) the speed of the arrow is again v₀.
D) the speed of the arrow is v₀.
E) the speed of the arrow is v₀/ .

Question 23

For which value of θ is the range of a projectile fired from ground level a maximum?

A) 30° above the horizontal
B) 45° above the horizontal
C) 55° above the horizontal
D) 60° above the horizontal
E) 90° above the horizontal

Question 24

A projectile is launched with initial velocity v₀ at an angle of 30° above the horizontal. If a second projectile is launched with the same initial velocity but at angle of 60° above the horizontal.

A) The range of the second projectile will be twice that of the first.
B) The range of the second projectile will be 1.41 that of the first.
C) The range of the second projectile will be one-half that of the first.
D) The ranges of the two projectiles will be identical.
E) It is impossible to compare the ranges of the two projectiles.

Question 25

A rock is thrown upwards at an angle of 40° with respect to the horizontal. As the rock is rising in its trajectory, the horizontal component of its velocity

A) increases.
B) decreases.
C) remains the same.
D) is zero.
E) Cannot be determined without additional information.

Question 26

A monkey is sitting at the top of a tree 20 m high from the ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food?

A) He should aim it at the monkey.
B) He should aim it below the monkey.
C) He should aim it above the monkey.
D) None of the other choices is correct.

Question 27

When a football in a field goal attempt reaches its maximum height, how does its speed compare to its initial speed?

A) It is zero.
B) It is less than its initial speed.
C) It is equal to its initial speed.
D) It is greater than its initial speed.
E) Cannot be determined without additional information.

Question 28

A student kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory:

A) both velocity and acceleration of the soccer ball are zero.
B) neither the ball's velocity nor its acceleration is zero.
C) the ball's acceleration is zero but not its velocity.
D) the ball's acceleration points upwards.
E) the ball's velocity points downwards.

Question 29

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. The magnitude of the acceleration of the ball while it is in flight is

A) 25 m/s².
B) 20 m/s².
C) 9.8 m/s².
D) 8.4 m/s².
E) 0 m/s².

Question 30

A ball is thrown with a velocity of 40 m/s at an angle of 30° above the horizontal and attains a certain range R. At what other angle will this ball attain the same range keeping its initial velocity the same?

A) 15°
B) 90°
C) 120°
D) 60°
E) All other angles will give different ranges.

Question 31

A rock is thrown from ground level at some angle above the horizontal with a certain velocity. It reaches its highest point and starts falling down. What is the magnitude of the velocity of the rock right before it hits the ground?

A) It is equal to its initial vertical velocity.
B) It is equal to its initial horizontal velocity.
C) It is equal to the magnitude of its initial velocity.
D) 0
E) Cannot be determined without additional information.

Question 32

An athlete throws a ball with a velocity of 40 m/s at an angle of 20° above the horizontal. Which of the following statements is true in this case?

A) The vertical component of the velocity remains constant.
B) The horizontal component of the velocity changes.
C) The vertical component of the velocity changes sign after the ball attains its maximum height.
D) The horizontal component of the velocity changes sign after the ball attains its maximum height.
E) None of the given choices is correct.

Question 33

A projectile is launched with an initial velocity of 80 m/s at an angle of 30° above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration?

A) 80 m/s²
B) 40 m/s²
C) 9.8 m/s²
D) 0 m/s²
E) 4.9 m/s²

Question 34

A bullet is fired from ground level with a speed of 150 m/s at an angle 30.0° above the horizontal at a location where g = 10.0 m/s². What is the horizontal component of its velocity when it is at the highest point of its trajectory?

A) 0 m/s
B) 10 m/s
C) 75.0 m/s
D) 130 m/s
E) 150 m/s

Question 35

Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30°. When the snowballs reach the ground below,

A) Debra's snowball will stay in the air longer than Mary's.
B) Mary's snowball will stay in the air longer than Debra's.
C) Both snowballs will take the same amount of time to hit the ground.
D) Debra's snowball never hits the ground since it is thrown upwards.
E) Mary's snowball never hits the ground since it is thrown downwards.

Question 36

A rock is thrown upwards at an angle of 40° with respect to the horizontal. As the rock is rising in its trajectory, the vertical component of its velocity

A) increases.
B) decreases.
C) remains the same.
D) is zero.
E) Cannot be determined without additional information.

Question 37

Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30°. When the snowballs reach the ground below,

A) Debra's snowball will have a higher speed than Mary's.
B) Mary's snowball will have a higher speed than Debra's.
C) Both snowballs will hit the ground with the same speed.
D) Debra's snowball never hits the ground since it is thrown upwards.
E) Mary's snowball never hits the ground since it is thrown downwards.

Question 38

A bullet is fired from ground level with a speed of 150 m/s at an angle 30.0° above the horizontal at a location where g = 10.0 m/s². What is the vertical component of its velocity when it is at the highest point of its trajectory?

A) 0 m/s
B) 10 m/s
C) 75.0 m/s
D) 130 m/s
E) 150 m/s

Question 39

A monkey is sitting at the top of a tree 20 m high from the ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the monkey remains seated at the top of the tree, how should the person aim the arrow containing the food so that the monkey gets the food?

A) He should aim it at the monkey.
B) He should aim it below the monkey.
C) He should aim it above the monkey.
D) None of the other choices is correct.

Question 40

For which value of θ is the height of a projectile fired from ground level a maximum?

A) 30° above the horizontal
B) 45° above the horizontal
C) 55° above the horizontal
D) 60° above the horizontal
E) 90° above the horizontal

Question 41

The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. How long does it take for the football to rise to the highest point of its trajectory?

A) 1.0 s
B) 2.0 s
C) 3.0 s
D) 4.0 s
E) 5.0 s

Question 42

A projectile is fired from ground level with an initial speed of 55.6 m/s at an angle of 41.2° above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.
(b) Determine the maximum height reached by the projectile.
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height.
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height.

Question 43

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the initial velocity of the bullet?

A) 86.6 m/s
B) 50.0 m/s
C) 36.6 m/s
D) 100 m/s
E) 136 m/s

Question 44

A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. How long is the jumper in the air before returning to the Earth?

A) 0.21 s
B) 0.42 s
C) 0.84 s
D) 1.3 s
E) 1.6 s

Question 45

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.00 m. How far from the edge of the table, measured along the floor, does the puck hit the floor?

A) 20.0 m
B) 40.0 m
C) 12.8 m
D) 19.6 m
E) 6.4 m

Question 46

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. At what angle is the bullet fired above the horizontal?

A) 45.0°
B) 60.0°
C) 30.0°
D) 90.0°
E) 75.0°

Question 47

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet gets to the highest point of its trajectory?

A) 5.0 seconds
B) 10.0 seconds
C) 15.0 seconds
D) 20.0 seconds
E) None of the other choices is correct.

Question 48

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground?

A) 20.0 m/s
B) 6.26 m/s
C) 12.5 m/s
D) 19.6 m/s
E) 21 m/s

Question 49

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s. The height of the table above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

A) 77.2°
B) 72.6°
C) 12.8°
D) 12.6°
E) 31.8°

Question 50

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. What is the range of the bullet?

A) 500 m
B) 1000 m
C) 100 m
D) 866 m
E) 433 m

Question 51

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the horizontal velocity of the ball just before it touches the ground?

A) 35 m/s
B) 9.8 m/s
C) 20 m/s
D) 4.9 m/s
E) 70 m/s

Question 52

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the initial speed of the ball?

A) 9.8 m/s
B) 20 m/s
C) 35 m/s
D) 4.9 m/s
E) 70 m/s

Question 53

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground?

A) 21 m/s
B) 22 m/s
C) 24 m/s
D) 25 m/s
E) 6.3 m/s

Question 54

A jumper in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. How far does the jumper jump?

A) 3.4 m
B) 6.2 m
C) 9.4 m
D) 15 m
E) 18 m

Question 55

A ball rolls off the edge of a table with an initial velocity of 20 m/s. The height of the table above the ground is 2.0 m. How long does it take the ball to reach the ground?

A) 0.49 s
B) 0.98 s
C) 0.64 s
D) 2.0 s
E) 0.32 s

Question 56

A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. How long does it take for the ball to hit the ground?

A) 0.29 s
B) 0.57 s
C) 1.14 s
D) 2.0 s
E) 9.8 s

Question 57

A ball is thrown horizontally with an initial velocity of 40 m/s from a height of 10 m. How long will it take for the ball to touch the ground? Use g = 10 m/s².

A) 0.70 second
B) 1.0 second
C) 2.0 seconds
D) 1.4 seconds
E) 2.4 seconds

Question 58

The horizontal and vertical components of the initial velocity of a football are 24 m/s and 7 m/s respectively. What is the initial velocity of the football?

A) 31 m/s
B) 25 m/s
C) 17 m/s
D) 42 m/s
E) 625 m/s

Question 59

A bullet is fired with a certain velocity at an angle θ above the horizontal at a location where g = 10.0 m/s². The initial x- and y-components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long does it take before the bullet hits the ground?

A) 5.0 seconds
B) 10.0 seconds
C) 15.0 seconds
D) 20.0 seconds
E) None of the other choices is correct.

Question 60

A projectile is shot horizontally at 23.4 m/s from the roof of a building 55.0 m tall.
(a) Determine the time necessary for the projectile to reach the ground below.
(b) Determine the distance from the base of the building that the projectile lands.
(c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.

Question 61

A projectile is shot from the edge of a vertical cliff 60.0 m above the ocean. It has a speed of 100 m/s and is fired at an angle of 35.0° below the horizontal. How far from the foot of the vertical cliff does the projectile hit the water?

A) 79.1 m
B) 312 m
C) 684 m
D) 1084 m
E) 540 m

Question 62

A ball is thrown at an angle θ above the horizontal. In the presence of the acceleration due to gravity, how far below the straight-line path following its original direction of motion will the ball be at the end of 1.0 second?

A) 20 m
B) 4.9 m
C) 9.8 m
D) 2.5 m
E) None of the other choices is correct.

Question 63

A bullet is fired from ground level with a speed of 150 m/s at an angle 30.0° above the horizontal at a location where g = 10.0 m/s². What is the vertical component of its velocity after 4 seconds?

A) 150 m/s
B) 35 m/s
C) 130 m/s
D) 75.0 m/s
E) 37.5 m/s

Question 64

A bullet is fired from ground level with a speed of 150 m/s at an angle 30.0° above the horizontal at a location where g = 10.0 m/s². What is the horizontal component of its velocity after 4 seconds?

A) 150 m/s
B) 35 m/s
C) 130 m/s
D) 75.0 m/s
E) 37.5 m/s

Question 65

A ball is thrown horizontally from the top of a building. What will be its vertical displacement from the top of building 2.0 seconds after it leaves your hands?

A) 4.9 m
B) 9.8 m
C) 19.6 m
D) 40.2 m
E) 52.4 m

Question 66

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. How far from where the child is standing does the ball hit the ground?

A) 1.22 m
B) 5.14 m
C) 6.79 m
D) 7.46 m
E) 1.58 m

Question 67

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. At what angle below the horizontal does the ball approach the ground?

A) 35.1°
B) 38.6°
C) 48.0°
D) 40.0°
E) 65.2°

Question 68

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. How long is the ball in flight before it hits the ground?

A) 1.22 s
B) 6.79 s
C) 7.45 s
D) 9.14 s
E) 2.44 s

Question 69

An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is to be dropped from the airplane to land on a target on the ground. At what horizontal distance away from the target should the package be released so that it lands on the target?

A) 2.55 km
B) 125 m
C) 326 m
D) 786 m
E) 1.22 km

Question 70

An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is to be dropped from the airplane to land on a target on the ground. In what direction will the package be traveling when it hits the ground?

A) 49.3° below horizontal
B) 62.7° below horizontal
C) 54.8° below horizontal
D) 84.2° below horizontal
E) 32.1° below horizontal

Question 71

A person throws a ball horizontally from the top of a building that is 40.0 m high. The initial velocity of the ball is 100 m/s. What is the horizontal distance that the ball travels before hitting the ground?

A) 100 m
B) 286 m
C) 325 m
D) 367 m
E) 572 m

Question 72

A ball is thrown horizontally with an initial velocity of 20.0 m/s from the edge of a building of a certain height. The ball lands at a horizontal distance of 82.0 m from the base of the building. What is the height of the building?

A) 40.5 m
B) 60.2 m
C) 87.9 m
D) 82.4 m
E) 50.4 m

Question 73

A boy kicks a football with a certain initial velocity at an angle 20° above the horizontal. In 2.0 seconds, the ball reaches at its highest point in its trajectory. What is the initial velocity of the ball?

A) 9.8 m/s
B) 20 m/s
C) 57 m/s
D) 4.9 m/s
E) 29 m/s

Question 74

A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. How high above the projection point is the ball after 2.0 s?

A) 5.4 m
B) 13 m
C) 25 m
D) 43 m
E) 50 m

Question 75

A child is trying to throw a ball over a fence. She gives the ball an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground and the fence is 2.00 m high. The ball just clears the fence while still traveling upwards. How far is the child from the fence?

A) 0.732 m
B) 1.58 m
C) 2.69 m
D) 3.81 m
E) 7.46 m

Question 76

A projectile is shot from the edge of a vertical cliff 60.0 m above the ocean. It has a speed of 100 m/s and is fired at an angle of 35.0° above the horizontal. How far from the foot of the vertical cliff does the projectile hit the water?

A) 126 m
B) 312 m
C) 684 m
D) 1080 m
E) 540 m

Question 77

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. What is the magnitude of the ball's velocity just before it hits the ground?

A) 1.22 m/s
B) 6.79 m/s
C) 7.45 m/s
D) 9.14 m/s
E) 4.58 m/s

Question 78

A ball is thrown with an initial speed of 60 m/s at an angle of 30° above the horizontal. What is the ball's horizontal displacement at the end of 4 seconds? Use g = 10 m/s².

A) 240 m
B) 60 m
C) 120 m
D) 210 m
E) 140 m

Question 79

A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the vertical component of its velocity at the highest point of its trajectory?

A) 0 m/s
B) 9.8 m/s
C) 19.6 m/s
D) 4.9 m/s
E) 17 m/s

Question 80

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball?

A) 202 m/s
B) 9.80 m/s
C) 19.6 m/s
D) 45.2 m/s
E) 94.4°