Question 1

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.

Accepted Answer

Since the plane is flying horizontally at a constant speed and drops the package, the package will continue to move horizontally at the same speed as the plane due to inertia. Therefore, when the package reaches the ground, the plane will be directly above it.

Question 2

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^oand 50^o C) 20^o and 30^o D) 30^o and 50^o E) 30^o and 70^o

Accepted Answer

The range of a projectile (like a javelin) thrown with a given initial speed is the same for complementary angles. The sum of complementary angles is 90 degrees. Therefore, 20 degrees and 70 degrees are complementary (20 + 70 = 90), and the javelin will land at the same distance for these two angles.

Question 3

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.

Accepted Answer

The range of a projectile launched at an angle θ from the horizontal is given by the formula $R = \frac{v^2 \sin 2\theta}{g}$, where $v$ is the initial speed and $g$ is the acceleration due to gravity. For angles complementary to each other (such as 30° and 60°), the range is the same because $\sin 2\theta$ yields the same value (for example, $\sin 60° = \sin 120°$). Therefore, the statement that the range of A is less than the range of B is incorrect, as both have equal ranges.

Question 4

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.

Accepted Answer

When a rifle's sight is adjusted for more distant targets, aiming directly at a closer target will result in the bullet hitting above the center. This is because the sight adjustment compensates for bullet drop over distance, which does not occur as much over shorter distances.

Question 5

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.

Accepted Answer

The acceleration of both projectiles A and B is due to gravity alone, which is the same for both regardless of the launch angle. Therefore, the ratio of their accelerations is 1.

Question 6

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.

Accepted Answer

The answer of Two shells are fired simultaneously from the...

Question 7

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.

Accepted Answer

Projectile A reaches the ground first because it is launched at a lower angle, resulting in a shorter time of flight compared to projectile B, which is launched at a higher angle and stays in the air longer.

Question 8

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.

Accepted Answer

The velocities of projectiles A and B just before impact are the same because they were launched at the same speed and their launch angles are symmetrical with respect to the horizontal. The effects of gravity on their speeds are identical but in opposite directions, leading to them having the same speed upon impact.

Question 9

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.

Accepted Answer

The car experiences a nonzero acceleration due to the change in direction of its velocity as it moves along the circular path, even if its speed remains constant. This is an example of centripetal acceleration.

Question 10

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.

Accepted Answer

An object moving at a constant speed in a circular path experiences centripetal acceleration, which changes the direction of its velocity without changing its speed, thus maintaining a circular path.

Question 11

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

Accepted Answer

The answer of A ball is rolling on a table...

Question 12

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.

Accepted Answer

The acceleration of the child at the top of the Ferris wheel points vertically downward due to gravity and the centripetal acceleration needed to keep the child moving in a circular path.

Question 13

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.

Accepted Answer

The centripetal acceleration is given by $a_c = \frac{v^2}{r}$. When the speed is halved, the new speed is $v/2$, so the new acceleration is $\frac{(v/2)^2}{r} = \frac{v^2}{4r}$, which is a fourth of the original centripetal acceleration.

Question 14

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.

Accepted Answer

The acceleration of a car traveling on a circular track with constant speed is directed toward the center of the track. This is known as centripetal acceleration, which is always directed towards the center of the circle along which the object is moving.

Question 15

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.

Accepted Answer

The bag sliding and hitting the passenger door is a result of inertia, where the bag tries to maintain its motion in a straight line while the car turns, according to Newton's first law of motion.

Question 16

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.

Accepted Answer

The magnitude of the train's centripetal acceleration decreases as the radius of the curve increases, given that the speed remains constant. This is because centripetal acceleration is inversely proportional to the radius of the curve (a_c = v^2/r).

Question 17

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.

Accepted Answer

Centripetal acceleration is given by the formula $a_c = \frac{v^2}{r}$, where $v$ is the velocity and $r$ is the radius of the circular path. If the speed ($v$) increases and the radius ($r$) remains constant, the magnitude of the centripetal acceleration ($a_c$) increases.

Question 18

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.

Accepted Answer

The direction of a car's centripetal acceleration when moving in a circle at constant speed is always radially inward towards the center of the circle, regardless of the curve's orientation or the car's speed.

Question 19

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.

Accepted Answer

The answer of A ball is connected by two massless...

Question 20

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.

Accepted Answer

The answer of A ball is connected by two massless...

Quiz 4: Motion in Two and Three Dimensions

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

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?

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

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

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

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?

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?

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 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

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

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 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

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

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

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

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

Quiz 4: Motion in Two and Three Dimensions

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

An athlete throws a javelin at four different angles (20o, 30o, 50o, and 70o) 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?

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

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

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

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?

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?

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 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

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

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 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

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

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

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

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

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?

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