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

FRQ 4 – Qualitative/Quantitative Translation
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Unit 1: Kinematics
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Practice FRQ 1 of 141/14

4. A student stands on a platform that moves horizontally to the right with constant speed v_p = 3.0 m/s. The student throws a ball with an initial speed of v_0 = 5.0 m/s at an angle of 37° above the horizontal, as measured in the reference frame of the platform. The ball is released at a height h = 2.0 m above the ground, as shown in Figure 2. Neglect air resistance.

Figure 2. Side view of ball trajectory

Side view showing platform at height h = 2.0 m above ground moving horizontally to the right. Ball trajectory shown as parabolic path from release point to ground. Initial velocity vector v_0 at 37° above horizontal. Height h labeled with vertical arrow from ground to release point.
A.

The time the ball is in the air in Scenario 1 is t_1, and the time the ball is in the air in Scenario 2 is t_2, both as measured in the ground reference frame.

Indicate whether t_1 is greater than, less than, or equal to t_2 by writing one of the following.

  • t_1 > t_2
  • t_1 < t_2
  • t_1 = t_2

Justify your answer using qualitative reasoning beyond referencing equations.

Figure 1. Top view of two scenarios

Two side-by-side top-view diagrams. Left diagram (Scenario 1): Platform moving right with velocity v_p. Student on platform throws ball to the right at angle 37° relative to platform motion direction. Right diagram (Scenario 2): Platform moving right with velocity v_p. Student on platform throws ball to the left at angle 37° relative to opposite of platform motion direction. Both show landing positions d_1 and d_2 measured from point directly below release.
B.

Derive an expression for the horizontal distance d_1 that the ball travels before landing, as measured in the ground reference frame, as shown in Figure 1. Express your answer in terms of v_p, v_0, θ, h, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider Scenario 1 only.

C.

Indicate whether the magnitude |v_x1| is greater than, less than, or equal to the magnitude |v_x2|. An observer on the ground measures the horizontal component of the ball's velocity just before it lands in Scenario 1 to be v_x1, and in Scenario 2 to be v_x2.

Briefly justify your answer.

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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 carefullybefore responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
  • Use the timer to practice time management. You can pause, restart, or hide the timer as needed.
  • Mark for Review if you want to come back to a question later.
  • Your responses are saved automatically as you type. You can also use the drawing tool for questions that require diagrams or graphs.
  • Use the toolbar for formatting options like bold, italic, subscript, and superscript.
  • Navigate between questions using the Previous and Next buttons at the bottom of the screen.

Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.