Deck 4: Motion in Two and Three Dimensions

Question 1

At a certain instant, a car's velocity points northward. Its acceleration

A) is zero.
B) points eastward.
C) points westward.
D) points southward.
E) may be zero or may point in any direction.

Answer 1

may be zero or may point in any direction.

Question 2

A toy car, initially moving along the y axis at 5.00 m/s, is accelerated uniformly for 10.0 s at 2.00 m/s² along the x axis. The magnitude of the toy car's displacement at the end of the 10.0 s is

A) 50.0 m.
B) 100 m.
C) 112 m.
D) 150 m.

Answer 2

112 m.

Question 3

A toy car moving along the x axis at 3.0 m/s is accelerated uniformly for 4.0 s at 0.40 m/s² along the y axis. The toy car's speed at the end of the 4.0 s is:

A) 1.0 m/s.
B) 1.4 m/s.
C) 3.0 m/s.
D) 3.4 m/s.
E) 4.6 m/s.

Answer 3

3.4 m/s.

Question 4

A train is traveling east at 30 km/h. After it rounds a curve, it travels south at 40 km/h. The magnitude of its average acceleration is

A) 10 km/h.
B) 35 km/h.
C) 50 km/h.
D) 70 km/h.

Question 5

A car travels one lap around a circular track in 120 s. The diameter of the track is 30 m. The car's average speed is

A) 0.0 m/s.
B) 0.13 m/s.
C) 0.25 m/s.
D) 1.6 m/s.

Question 6

A girl runs around a circular track of radius R with a constant speed v. At the moment the girl has run half of the track, the magnitude of her average velocity is

A) $\mathcal { V }$
B) $0$
C) 2v/. $\pi$
D) $2 v$
E) 2v. $\pi$

Question 7

A girl runs around a circular track of radius R with a constant speed v. At the moment the girl has run half of the track, the magnitude of her average acceleration is

A) v²/ $\pi$ R.
B) $0$
C) 2v²/R.
D) 2v²/ $\pi$ R.
E) v²/R.

Question 8

An arrow is shot into the air. While in the air, the arrow's acceleration is due to

A) gravity and the forward push.
B) gravity and the upward lift.
C) the forward push.
D) the upward lift.
E) gravity.

Question 9

For the two-dimensional motion of a projectile, all of the following apply except

A) the path is a parabola.
B) the maximum range occurs when the launch angle is 45°.
C) the maximum height occurs at the midpoint of the flight.
D) the time of flight to half the maximum height is equal to 1/4 the total time of flight.

Question 10

You want to aim a water gun so that the water travels the maximum horizontal distance. The angle you aim at is

A) 0^o.
B) 30^o.
C) 45^o.
D) 60^o.
E) 90^o.

Question 11

Two racquets hit two tennis balls at the same speed and angle-one on the Earth and the other on the Moon. Because the acceleration due to gravity on the Moon is six times smaller than on the Earth, the ball on the Moon would travel

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

Question 12

A basketball is shot from a free-throw range. At the top of the basketball's trajectory, its acceleration is

A) zero.
B) equal to the acceleration due to gravity.
C) less than the acceleration due to gravity.
D) more than the acceleration due to gravity.
E) unknown; more information is needed to work out the answer.

Question 13

A projectile is fired at 25^o above the horizontal. At the highest point in its trajectory, its speed is 100 m/s. If air resistance is ignored, the initial velocity had a horizontal component of

A) 0 m/s.
B) 100 cos(25^o) m/s.
C) 100 sin(25^o) m/s.
D) 100 m/s.
E) 100/sin(25^o) m/s.

Question 14

A baseball is hit by a bat and is launched in a projectile motion at 30^o above the horizontal. At the top of the baseball's trajectory

A) its acceleration is zero and its velocity is nonzero.
B) both its acceleration and its velocity are zero.
C) its acceleration is nonzero and its velocity is zero.
D) its acceleration is nonzero and its velocity is nonzero.

Question 15

For the two-dimensional motion of a projectile launched from the ground, all of the following apply except

A) the total travel distance of the projectile in the air is greater than the straight paths connecting the launch point, the maximum height point, and the final impact point.
B) the vertical component of velocity is never greater than at the instant of launching.
C) the minimum speed occurs at the midpoint in time of the flight.
D) the time of flight to half the maximum height is greater than 1/4 the total time of flight.

Question 16

A yellow ball rolling rapidly along a tabletop rolls off the edge and falls to the floor. At the same instant, a blue ball having the same mass and shape as the yellow one is dropped from the same height. The ball that reaches the floor first is

A) the yellow ball.
B) the blue ball.
C) neither; both reach the floor at the same time.
D) unknown; one needs to know the speed of the yellow ball just before it rolls off the edge to work out the answer.

Question 17

A yellow ball rolling rapidly along a tabletop rolls off the edge and falls to the floor. At the same instant, a blue ball having the same mass and shape as the yellow one is dropped from the same height. The ball that has the larger vertical velocity component when it hits the floor is

A) the yellow ball.
B) the blue ball.
C) neither; both have the same vertical velocity component.
D) unknown; one needs to know the speed of the yellow ball just before it rolls off the edge to work out the answer.

Question 18

If the initial speed of a projectile is doubled, its time of flight would

A) be four times smaller.
B) be two times smaller.
C) remain unchanged.
D) be two times larger.
E) be four times larger.

Question 19

A ball is thrown at an original speed of 6.0 m/s at an angle of 30^o above the horizontal. The speed of the ball when it returns to the same horizontal level is

A) 12 m/s.
B) 6.0 m/s.
C) 3.0 m/s.
D) 9.8 m/s.
E) 4.9 m/s.

Question 20

A ball leaves the hand of a boy with a velocity v and travels a horizontal range R. In a second throw, the same ball leaves the boy's hand with a velocity of 2v. Compared to the first throw, the horizontal range is

A) the same.
B) two times larger.
C) half as large.
D) four times larger.
E) a fourth of the first.

Question 21

A pilot drops a package of food and water supplies from a plane that is flying horizontally at constant speed. When the package reaches the ground, the plane's horizontal position relative to the package

A) is directly above the package.
B) is behind the package.
C) is in front of the package.
D) depends on the mass of the package.
E) is unknown; more information is needed to work out the answer.

Question 22

An athlete throws a javelin at four different angles (20^o, 30^o, 50^o, and 70^o) above the horizontal, all with the same initial speed. For which two angles will the javelin land at the same distance from the throwing point?

A) 20^o and 70^o
B) 20^o and 50^o
C) 20^o and 30^o
D) 30^o and 50^o
E) 30^o and 70^o

Question 23

Consider two projectiles A and B launched at angles 30^o and 60^o from the horizontal with equal initial speeds. All of the following statements are correct except

A) the flight time of A is less than the flight time of B.
B) the range of A is less than the range of B.
C) the maximum height reached by A is less than the maximum height reached by B.
D) the maximum vertical velocity component of A is less than the maximum vertical velocity component of B.

Question 24

An expert marksman aims a high-speed rifle directly at the center of a nearby target. The rifle's sight has been adjusted for more distant targets. The bullet will hit the target

A) above the center of the target.
B) right at the center of the target.
C) below the center of the target.
D) to the left or right of the center of the target.
E) at an unknown location; more information is needed to work out the answer.

Question 25

Two projectiles, A and B, are launched with equal initial speeds. Projectile A is launched at angle 35° and projectile B at angle 55° above the horizontal. The ratio of the acceleration of A to that of B is

A) greater than 1.
B) equal to 1.
C) less than 1.
D) zero.
E) unknown; more information is needed to work out the answer.

Question 26

Two shells are fired simultaneously from the same battleship at two targets. The shells follow the trajectories shown here. Which target will be hit first?

A) Target 1
B) Target 2
C) Both targets will be hit at the same time.
D) More information is needed to work out the answer.

Question 27

Two projectiles, A and B, are launched with equal initial speeds. Projectile A is launched at angle 35° and projectile B at angle 55° above the horizontal. Which projectile reaches the ground first?

A) A because it travels faster horizontally.
B) B because it travels faster horizontally.
C) They both reach the ground at the same time.
D) A because it stays above the ground longer.
E) B because it stays above the ground longer.

Question 28

Two projectiles, A and B, are launched with the same speed from a tower. Projectile A is launched at an angle of 30° above the horizontal, and projectile B at an angle of 30° below the horizontal. Just before their impact point

A) the velocity of A is larger than the velocity of B.
B) the velocity of A is the same as the velocity of B.
C) the velocity of A is smaller than the velocity of B.
D) both velocities are zero.

Question 29

A roller coaster car travels at a constant speed on a track that forms a circular loop in a vertical plane. The car's acceleration is

A) zero.
B) nonzero.

Question 30

Is it possible for an object moving at a constant speed around a circular path to be subject to an acceleration?

A) No: The path would not be a circle.
B) No: An object can have only one or the other at any given time.
C) Yes, this is possible.
D) More information is needed to work out the answer.

Question 31

A ball is rolling on a table in a partial hoop (shown here as seen looking down on the tabletop). The path of the ball after it leaves the hoop is best described by which of the following arrows?

A) A
B) B
C) C
D) D

Question 32

A child is riding on a Ferris wheel that is rotating clockwise at a constant speed. When the child is at the top of the wheel, her acceleration

A) points vertically downward.
B) points vertically upward.
C) points horizontally toward the right.
D) has a downward vertical component and a horizontal component pointing right.
E) has a downward vertical component and a horizontal component pointing left.

Question 33

An object is undergoing uniform circular motion. Its speed is 10 m/s and the radius of its path is 15 m. When its speed is halved, its centripetal acceleration is

A) four times larger than the original centripetal acceleration.
B) twice as large as the original centripetal acceleration.
C) the same as the original centripetal acceleration.
D) half of the original centripetal acceleration.
E) a fourth of the original centripetal acceleration.

Question 34

A car travels on a circular track with a constant speed. The acceleration of the car is

A) directed forward in the direction of travel.
B) directed toward the center of the track.
C) directed toward the center of the Earth.
D) zero because the car travels at constant speed.
E) none of the above.

Question 35

A student driving her car at a constant speed makes a left turn. Her bag, on the passenger seat, slides and hits the passenger door. Which statement is correct?

A) The bag was pushed toward the door because it experienced a centripetal acceleration.
B) The bag was not pushed toward the door. It just tried to maintain its motion at constant speed in a straight line.
C) The bag was pushed toward the door because it was too heavy.
D) None of these explanations is true.

Question 36

A train travels around a curve of increasing radius at a constant speed. The magnitude of the train's centripetal acceleration

A) decreases.
B) remains constant.
C) increases.
D) is zero.
E) is unknown; more information is needed to work out the answer.

Question 37

A boy runs around a circular track of constant radius at an increasing speed. The magnitude of his centripetal acceleration

A) decreases.
B) increases.
C) is zero.
D) is unknown; more information is needed to work out the answer.

Question 38

A car travels around a curve of constant radius at a constant speed. The direction of the car's centripetal acceleration is

A) horizontal.
B) vertical.
C) tangent to the curve, and points in the same direction as the car is moving.
D) radially inward.
E) unknown; more information is needed to work out the answer.

Question 39

A ball is connected by two massless strings to a vertical, rotating rod, and it moves in a horizontal circle. The strings are tied to the rod, are taut, and form two sides of an equilateral triangle. A photograph of the system is taken at moment t and is shown in the figure here. At t the centripetal acceleration of the ball is

A) horizontal and points right.
B) horizontal and points left.
C) zero.
D) vertical and points upward.
E) vertical and points downward.

Question 40

A ball is connected by two massless strings to a horizontal, rotating rod, and moves in a vertical circle. The strings are tied to the rod, are taut, and form two sides of an equilateral triangle. A photograph of the system is taken at moment t and is shown in the figure here. At t the centripetal acceleration of the ball is

A) horizontal and points right.
B) horizontal and points left.
C) zero.
D) vertical and points upward.
E) vertical and points downward.

Question 41

The velocity of an object with respect to reference frame A is equal to

A) the velocity of the object with respect to reference frame B added vectorially to the velocity of reference frame A with respect to reference frame B.
B) the velocity of the object with respect to reference frame B added vectorially to the velocity of reference frame B with respect to reference frame A.
C) Both of the first two responses are correct.
D) Neither of the first two responses is correct.

Question 42

If reference frame A is in motion with respect to reference frame B, the velocity of an object with respect to frame A

A) cannot equal the velocity of the object with respect to frame B.
B) may or may not equal the velocity of the object with respect to frame B.
C) must equal the velocity of the object with respect to frame B.
D) None of the previous answers is correct.

Question 43

A boat is trying to cross a river that flows due north with a strong current. The boat starts at point A on the west bank and will reach the east bank directly across from the starting point. The boat should head

A) south.
B) southwest.
C) southeast.
D) west.
E) east.

Question 44

A boy is shooting marbles on a flatcar that is itself in uniform motion on a straight, horizontal track. The boy can shoot marbles at a speed of 30 m/s with respect to the flatcar. The speed of the flatcar with respect to the train track rails is 40 m/s. The maximum possible horizontal speed of a marble with respect to the rails is

A) 10 m/s.
B) 30 m/s.
C) 40 m/s.
D) 50 m/s.
E) 70 m/s.

Question 45

A car travels due east with a speed of 40.0 km/h. Raindrops are falling at a constant speed of 30.0 km/h vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of

A) 53.0° with the vertical.
B) 53.0° with the horizontal.
C) 0.0° with the vertical.
D) 0.0° with the horizontal.

Question 46

An airplane having a speed relative to the air of 250 km/h needs to land in a city north of the departure airport when the wind blows toward the east at 40 km/h. The pilot should maintain a heading of

A) 79.9°.
B) 10.1°.
C) 0°.
D) 10.2°.
E) 79.8°.

Question 47

A boat travels at a constant speed with respect to still water. Now suppose the water is moving with respect to the bank at a speed almost as large as the speed of the boat with respect to still water. Compare the time taken for a round trip of constant distance (with respect to the bank) in the boat under two scenarios: downstream, then upstream or cross-stream, then back. The "down-up" time is

A) larger than the "across-back" time.
B) equal to the "across-back" time.
C) less than the "across-back" time.

Question 48

A boat travels at a constant speed with respect to still water. The water is moving with respect to the bank at a speed almost as large as the speed of the boat with respect to still water. Assume a round trip of constant distance (with respect to the bank) in the boat under two scenarios: downstream, then upstream or cross-stream, then back. All of the following statements are correct except

A) the speed of the boat when returning upstream is very small.
B) the cross-stream scenario involves a cross-stream component that is small, but much larger than the upstream speed of the boat.
C) the cross-stream time is independent of the stream speed compared to the boat speed.
D) the time spent traveling downstream is very small compared to other travel times in the problem.

Question 49

A school bus travels east at 40 km/h. Alex, sitting on the left side of the bus, throws a tennis ball at 30 km/h to Brendan, who is seated on the right side of the bus, directly across from Alex. The velocity of the ball as seen by Kyle, standing next to the road, is

A) 26 km/h, 46° east of north.
B) 26 km/h, 44° east of north.
C) 10 km/h, 54° east of north.
D) 50 km/h, 59° east of north.
E) 50 km/h, 31° east of north.

Question 50

A school bus travels east at 10 km/h. Alex, sitting in the back of the bus throws a tennis ball at Brendan. Kyle, standing next to the road, observes the ball moving at 60 km/h south. The direction of the velocity of the ball with respect to the bus is

A) 91° east of north.
B) 91° west of south.
C) 81° east of north.
D) 9.5° west of south.
E) 9.5° east of north.