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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 81/8

1. A small ball is launched from ground level with an initial velocity at an angle above the horizontal. The ball's initial velocity has a horizontal component of magnitude 3v₀ and a vertical component of magnitude 4v₀, where v₀ is a positive constant. The ball reaches its maximum height at time tₘ and lands on the ground at time tᴸ. Air resistance is negligible, and the gravitational acceleration has magnitude g.

Figure 1. Velocity-vector component grids for the projectile at three times (t = 0, t = tₘ, t = tᴸ).

Figure 1
A.
i.

The coordinate grids in Figure 1 can be used to represent the velocity vectors of the ball at three different times during its flight.

Draw arrows on the three grids to represent the velocity vectors at t = 0, t = tₘ, and t = tᴸ.

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Each arrow should start at the origin of its respective grid.

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The length and direction of each arrow should accurately represent the magnitude and direction of the velocity vector at that time.

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If the velocity has zero magnitude in any direction, the arrow should reflect this.

ii.

The vertical position of the ball as a function of time is given by y(t) = 4v₀t - (1/2)gt², where the upward direction is positive.

Derive an expression for the maximum height yₘₐₓ reached by the ball. Express your answer in terms of v₀, g, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 2. Projectile trajectory with labeled launch, peak, and landing points and axis directions.

Figure 2
B.

Describe the motion of the ball as observed in the reference frame of the moving observer. Your description should include the trajectory shape, the horizontal component of velocity, and the vertical component of velocity as functions of time in the observer's reference frame. Justify your answer using fundamental principles of relative motion. An observer moves horizontally with constant velocity vₒᵦₛ = 3v₀ in the +x-direction, as shown in Figure 2. The observer begins at the launch point when the ball is launched 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 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.
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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.