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⚙️AP Physics C: Mechanics
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⚙️AP Physics C: Mechanics

FRQ 1 – Mathematical Routines
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Unit 1: Kinematics
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Practice FRQ 1 of 101/10

1. A ball is launched from the edge of a cliff at time t = 0, as shown in Figure 1. The cliff is 80.0 m above the ground below. The ball is launched with an initial speed of 20.0 m/s at an angle of 37° above the horizontal. A train moves along the ground at the base of the cliff with a constant horizontal velocity of 15.0 m/s in the same horizontal direction as the ball's horizontal velocity component. An observer standing on the ground (Observer G) and an observer riding on the train (Observer T) both watch the ball's motion. Assume air resistance is negligible and take g = 10.0 m/s².

Figure 1. Ball launched from an 80.0 m cliff; train moving along the ground with speed 15.0 m/s; axes and initial velocity (20.0 m/s at 37°).

Figure 1
A.
i.

Describe the initial velocity of the ball as a vector quantity as measured by Observer G, including its horizontal and vertical components. Express your answer using the given values.

ii.

Derive expressions for the instantaneous horizontal position x(t)x(t)x(t) and vertical position y(t)y(t)y(t) of the ball as functions of time as measured by Observer G, taking the launch point as the origin, with +x in the direction of horizontal motion and +y upward. Express your answers in terms of the given numerical values and ttt. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

B.

Derive an expression for the time tlandt_{land}tland​ at which the ball reaches the ground as measured by Observer G. Express your answer in terms of the given numerical values. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

C.

Describe the initial velocity of the ball as measured by Observer T, including both the horizontal and vertical components. Explain how Observer T's measurement differs from Observer G's measurement and identify which component(s) of the ball's motion are the same in both reference frames. Observer T rides on the train, which moves at a constant horizontal velocity of 15.0 m/s in the +x direction. Observer T measures the ball's velocity relative to the train at t = 0.

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Free Response Question Practice

This practice environment simulates the AP AP Physics C: Mechanics Free Response Questions section. Here are some guidelines:

  • Read each question carefully before responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.