Deck 4: Two-Dimensional Kinematics

Question 1

Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice. )

A)The speed of the object is constant but its velocity is not constant.
B)The acceleration of the object is +g when the object is rising and -g when it is falling.
C)The acceleration of the object is zero at its highest point.
D)The speed of the object is zero at its highest point.
E)The horizontal acceleration is always zero and the vertical acceleration is always a non-zero constant downward.

Answer 1

The horizontal acceleration is always zero and the vertical acceleration is always a non-zero constant downward.

Question 2

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° above the horizontal.Which of the following statements are true about just before the snowballs reach the ground below? (There could be more than one correct choice. )

A)Debra's snowball will stay in the air longer than Mary's snowball.
B)Mary's snowball will stay in the air longer than Debra's snowball.
C)Both snowballs will take the same amount of time to hit the ground.
D)Debra's snowball has exactly the same acceleration as Mary's snowball.
E)Mary's snowball has a greater downward acceleration than Debra's snowball.

Answer 2

Debra's snowball will stay in the air longer than Mary's snowball.
Debra's snowball has exactly the same acceleration as Mary's snowball.

Question 3

In an air-free chamber,a pebble is thrown horizontally,and at the same instant a second pebble is dropped from the same height.Compare the times of fall of the two pebbles.

A)The thrown pebble hits first.
B)The dropped pebble hits first.
C)They hit at the same time.
D)We cannot tell without knowing which pebble is heavier.

Answer 3

They hit at the same time.

Question 4

A ball thrown horizontally from a point 24 m above the ground,strikes the ground after traveling horizontally a distance of 18 m.With what speed was it thrown,assuming negligible air resistance?

A)6.1 m/s
B)7.4 m/s
C)8.1 m/s
D)8.9 m/s

Question 5

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

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

Question 6

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 if there is no air resistance.

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 7

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

A)be behind the package.
B)be directly over the package.
C)be in front of the package.
D)depend on the speed of the plane when the package was released.

Question 8

For general projectile motion with no air resistance,the horizontal component of a projectile's velocity

A)remains zero.
B)remains a non-zero constant.
C)continuously increases.
D)continuously decreases.
E)first decreases and then increases.

Question 9

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° above the horizontal.Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice. )

A)Debra's snowball will have a higher speed than Mary's snowball.
B)Mary's snowball will have a higher speed than Debra's snowball.
C)Both snowballs will hit the ground with the same speed.
D)Both snowballs hit the ground at the same time.
E)Mary's snowball reaches the ground before Debra's snowball.

Question 10

A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal.If there is no air resistance,what is the speed of the ball when it returns to the same horizontal level?

A)4.0 m/s
B)8.0 m/s
C)16 m/s
D)9.8 m/s

Question 11

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.If there is no air resistance,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 must be 9.8 m/s larger than that of John.
E)the splashdown speed of John must be 25 m/s larger than that of James.

Question 12

A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal.If we can neglect air resistance,what is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

A)10 m/s
B)17 m/s
C)20 m/s
D)zero

Question 13

For general projectile motion with no air resistance,the vertical component of a projectile's acceleration

A)is always zero.
B)remains a non-zero constant.
C)continuously increases.
D)continuously decreases.
E)first decreases and then increases.

Question 14

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically.Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

A)It is impossible to tell because we do not know their masses.
B)the stone
C)the ball
D)Both are traveling at the same speed.

Question 15

A boulder rolls off of a very high cliff and experiences no significant air resistance.While it is falling,its trajectory is never truly vertical.

Question 16

For general projectile motion with no air resistance,the horizontal component of a projectile's acceleration

A)is always zero.
B)remains a non-zero constant.
C)continuously increases.
D)continuously decreases.
E)first decreases and then increases.

Question 17

A girl throws a rock horizontally,with a velocity of 10 m/s,from a bridge.It falls 20 m to the water below.How far does the rock travel horizontally before striking the water,assuming negligible air resistance?

A)14 m
B)16 m
C)20 m
D)24 m

Question 18

A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff.A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s.What is the height of the cliff if air resistance is negligibly small?

A)22 m
B)43 m
C)77 m
D)91 m

Question 19

The acceleration due to gravity on the Moon is only one-sixth of that on Earth,and the Moon has no atmosphere.If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle)as on Earth,how far would the ball would travel on the Moon compared to on Earth? Neglect air resistance on Earth.

A)1/6 as far as on Earth
B)36 times as far as on Earth
C)the same distance as on Earth
D)6 times as far as on Earth
E) as far as on Earth

Question 20

A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal.It reaches its highest point and starts falling down.Which of the following statements about the rock's motion are true just before it hits the ground? (There could be more than one correct choice. )

A)Its horizontal velocity component is zero.
B)Its velocity is vertical.
C)Its vertical velocity component is the same as it was just as it was launched.
D)Its horizontal velocity component is the same as it was just as it was launched.
E)Its speed is the same as it was just as it was launched.

Question 21

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 horizontal distance to the point where the football hits the ground if we neglect air resistance?

A)20 m
B)35 m
C)18 m
D)60 m
E)30.0 m

Question 22

You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance.After
,the magnitude of the velocity of the rock is closest to

A)28 m/s.
B)20 m/s.
C)40 m/s.
D)37 m/s.

Question 23

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35° above the horizontal.How long does the athlete stay in the air,assuming no significant air resistance?

A)0.50 s
B)0.88 s
C)1.1 s
D)2.5 s
E)0.54 s

Question 24

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/s horizontally in a city where the acceleration due to gravity is 9.81 m/s².The puck experiences no significant air resistance as it falls.The height of the platform 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 25

A child is trying to throw a ball over a fence.She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the horizontal.The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high.The ball just clears the fence while still traveling upwards and experiences no significant air resistance.How far is the child from the fence?

A)0.73 m
B)1.6 m
C)2.7 m
D)3.8 m
E)7.5 m

Question 26

A projectile is fired from ground level with a speed of 150 m/s at an angle 30° above the horizontal on an airless planet where g = 10.0 m/s².What is the horizontal component of its velocity after 4.0 s?

A)150 m/s
B)35 m/s
C)130 m/s
D)75 m/s
E)38 m/s

Question 27

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance.The height of the platform 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 m/s
B)6.3 m/s
C)13 m/s
D)15 m/s
E)21 m/s

Question 28

A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal.If air resistance is negligible,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 29

A boy throws a rock with an initial velocity of
At 30.0° above the horizontal.How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s²?

A)0.160 s
B)0.282 s
C)0.313 s
D)0.441 s

Question 30

In a room where g = 9.81 m/s²,a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally.The height of the platform above the ground is 2.00 m.What is the speed of the puck just before it hits the ground? The air resistance is negligibly small.

A)48.2 m/s
B)28.7 m/s
C)28.0 m/s
D)26.3 m/s
E)6.26 m/s

Question 31

A plane flying horizontally at a speed of 50 m/s and at an elevation of 160 m drops a package,and 2.0 s later it drops a second package.How far apart will the two packages land on the ground if air resistance is negligible?

A)100 m
B)160 m
C)180 m
D)320 m

Question 32

A ball rolls over the edge of a platform with only a horizontal velocity.The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m.What is the horizontal velocity of the ball just before it touches the ground? Neglect air resistance.

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

Question 33

A football kicker is attempting a field goal from
Out.The ball is kicked and just clears the lower bar with a time of flight of
If the angle of the kick was 45°,what was the initial speed of the ball,assuming no air resistance?

A)21.5 m/s
B)19.7 m/s
C)2.2 m/s
D)39 m/s

Question 34

A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally.The height of the platform above the ground is 2.0 m.What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air resistance.

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

Question 35

A cat leaps to try to catch a bird.If the cat's jump was at 60° off the ground and its initial velocity was
What is the highest point of its trajectory,neglecting air resistance?

A)0.29 m
B)0.58 m
C)10.96 m
D)0.19 m

Question 36

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m,as shown in the figure.The width of the pylon is very narrow,and the length of each propeller blade is 12 m.A tip of the propeller breaks off just when the propeller is vertical.The fragment flies off horizontally,falls,and strikes the ground at point P with negligible air resistance.Just before the fragment broke off,the propeller was turning uniformly,taking 1.2 s for each rotation.How far is point P from the base of the pylon?

A)120 m
B)130 m
C)140 m
D)150 m
E)160 m

Question 37

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55° with the vertical.What is the length of the athlete's jump if air resistance is of no significance?

A)0.88 m
B)8.0 m
C)12 m
D)17 m
E)4.0 m

Question 38

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? Neglect air resistance and use g = 9.81 m/s².

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

Question 39

A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal.What is the vertical component of its velocity after 4.0 s if air resistance is neglected?

A)150 m/s
B)36 m/s
C)130 m/s
D)75 m/s
E)38 m/s

Question 40

A fisherman casts his bait toward the river at an angle of 25° above the horizontal.As the line unravels,he notices that the bait and hook reach a maximum height of
What was the initial velocity he launched the bait with? Assume that the line exerts no appreciable drag force on the bait and hook and that air resistance is negligible.

A)18 m/s
B)7.9 m/s
C)7.6 m/s
D)6.3 m/s

Question 41

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

A)25 m/s².
B)18 m/s².
C)9.8 m/s².
D)8.5 m/s².
E)0 m/s².

Question 42

A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal.The ball leaves her hand 1.0 m above the ground.At what angle below the horizontal does the ball approach the ground?

A)35°
B)42°
C)48°
D)40°
E)65°

Question 43

A hobbyist launches a projectile from ground level on a horizontal plain.It reaches a maximum height of 72.3 m and lands 111 m from the launch point,with no appreciable air resistance.What was the angle of launch if g = 9.80 m/s²?

A)69.0°
B)67.4°
C)22.6°
D)44.8°

Question 44

A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s².The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively.At what angle was the projectile fired above the horizontal?

A)45°
B)60°
C)30°
D)90°
E)75°

Question 45

The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively.If there is no air resistance,how long does it take the football to reach the top of its trajectory?

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

Question 46

A projectile is fired from the edge of a cliff as shown in the figure.The initial velocity components are 940 m/s (horizontal)and 96 m/s (vertical).The projectile reaches maximum height at point P and then falls and strikes the ground at point Q.How high is point P above point Q,assuming no air resistance?

A)470 m
B)490 m
C)45,000 m
D)940 m
E)90,000 m

Question 47

A projectile is launched with an initial velocity of 80 m/s at 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)69 m/s²

Question 48

As shown in the figure,a projectile is fired at time t = 0.00 s,from point 0 at the upper edge of a cliff,with initial velocity components of
And
The projectile rises and then falls into the sea at point P.The time of flight of the projectile is
And air resistance is negligible.At this location,g = 9.80 m/s².What is the horizontal distance D?

A)2,250 m
B)2,520 m
C)2,790 m
D)3,060 m
E)3,330 m

Question 49

A projectile is fired from ground level at an angle above the horizontal on an airless planet 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 after firing does it take before the projectile hits the level ground?

A)5.00 seconds
B)10.0 seconds
C)15.0 seconds
D)20.0 seconds

Question 50

A projectile is fired from ground level on a horizontal plain.If the initial speed of the projectile is now doubled,and we neglect air resistance,

A)its range will be increased by .
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 51

An athlete participates in an interplanetary discus throw competition during an Olympiad that takes place on a planet where the acceleration due to gravity is 9.7 m/s².He throws the discus with an initial velocity of 20 m/s at an angle of 60° from the vertical.Neglecting air resistance and the height of the discus at the point of release,what is the range of the discus?

A)21 m
B)60 m
C)36 m
D)40 m
E)32 m