AP Physics C: Mechanics Practice Quiz: Reference Frames and Relative Motion

Correct Answer: B

The reference frame of an observer includes the observer and everything that is stationary relative to them. For an observer standing on the ground, their reference frame is the ground.

Correct Answer: B

In the passenger's reference frame (the train), the ball has no initial horizontal velocity relative to the passenger, so it appears to fall straight down. In the platform observer's reference frame, the ball has the same initial horizontal velocity as the train, so its path is a combination of forward motion and downward motion. This demonstrates how the motion of objects is measured differently by observers in different reference frames.

Correct Answer: C

The choice of reference frame (the shore) will determine the direction and magnitude of the measured velocity. The velocity of the boat relative to the shore is the combination of its velocity relative to the water and the water's velocity relative to the shore. Since these velocities are in different directions (east and south), the resultant velocity will have a different magnitude and direction than either individual velocity.

Correct Answer: D

The observed velocity results from the combination of the object's velocity (the person walking) and the velocity of the reference frame (the train). Since they are in the same direction, the velocities add. The velocity relative to the ground is 15 m/s + 2 m/s = 17 m/s. This demonstrates converting a measurement from the train's reference frame to the ground's reference frame.

Correct Answer: A

The observed velocity is the combination of the ball's velocity relative to the skateboard and the skateboard's velocity relative to the ground. Taking North as the positive direction, the skateboard's velocity is +5 m/s and the ball's velocity relative to the skateboard is -3 m/s. The combined velocity is +5 m/s + (-3 m/s) = +2 m/s, which is 2 m/s North.

Correct Answer: C

From the reference frame of Car A, its own velocity is considered zero. Car B is moving 10 m/s faster in the same direction. Therefore, an observer in Car A will measure Car B as moving east at 30 m/s - 20 m/s = 10 m/s. The motion of an object is described differently depending on the observer's reference frame.

Correct Answer: C

The provided content explicitly states that the choice of reference frame will determine the direction and magnitude of quantities measured by an observer. Therefore, the observers on the ship and the dock will measure different velocities for the same seagull because their reference frames are in motion relative to each other.

Correct Answer: A

The observed velocity is the combination of the person's velocity and the reference frame's velocity. Let's define upwards as the positive direction. The escalator's velocity is +0.5 m/s. The person's velocity relative to the escalator is downwards, so it's -1.5 m/s. The person's velocity relative to the ground is +0.5 m/s + (-1.5 m/s) = -1.0 m/s, which is 1.0 m/s downwards.

Correct Answer: B

As stated in the provided content, the choice of reference frame determines the direction and magnitude of quantities measured by an observer. An object's velocity is not absolute; its value is relative to the observer's frame of reference.

Correct Answer: B

The motion of an object is measured differently in different reference frames. While the cup is stationary in the reference frame of the train, the entire train (including the cup) is moving from the perspective of the ground observer. Therefore, the ground observer sees the cup moving with the same constant velocity as the train.

Correct Answer: B

The content states that measurements from a given reference frame may be converted to measurements from another reference frame. This conversion is achieved by accounting for the relative motion between the frames. The observed velocity of an object results from the combination of its velocity in one frame and the velocity of that frame relative to another.

Correct Answer: C

The observed velocity from the ground is the combination (vector sum) of the plane's velocity relative to the air and the air's velocity relative to the ground. The plane's velocity is a vector pointing north, and the wind's velocity is a vector pointing east. The resultant vector will point in a direction between north and east, and its magnitude (speed) will be the hypotenuse of a right triangle with sides 100 and 20. The speed is √(100² + 20²) which is approximately 102 m/s, a value greater than 100 m/s.

Correct Answer: C

The person's velocity relative to the ground (as seen by the stationary observer) is the combination of their walking velocity (their velocity relative to the walkway) and the velocity of the walkway itself (the velocity of their reference frame). This directly demonstrates the principle. The other options describe acceleration, a measurement within a single frame, and orbital mechanics, respectively.

Correct Answer: B

Measurements from different frames can be converted. Let V_b/g be the bird's velocity relative to the ground, V_b/c be the bird's velocity relative to the car, and V_c/g be the car's velocity relative to the ground. The relationship is V_b/g = V_b/c + V_c/g. We have 15 m/s East = 10 m/s East + V_c/g. Solving for V_c/g gives 15 - 10 = 5 m/s East.