AP Physics C: Mechanics FRQ Practice

⚙️AP Physics C: Mechanics

Practice FRQ 1 of 161/16

2. A student stands on the ground floor of a building and throws a ball upward at an angle from a height of 2.0 m above the ground. The ball is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal, as shown in Figure 1. The ball reaches a maximum height and then falls to the ground. Air resistance is negligible.

Figure 1. Ball launched from height 2.0 m with initial speed 15 m/s at 53°; elevator in adjacent building moves downward at 3.0 m/s.

Physics setup diagram with a clearly defined 2D coordinate system and labeled quantities.

Coordinate axes (must be prominent):
- Draw a horizontal x-axis and vertical y-axis that intersect at a single origin point on the ground line.
- Label the origin with the visible text "0".
- Add arrowheads on the positive ends of both axes.
- Label the positive horizontal direction "x" and the positive vertical direction "y".

Ground and launch height:
- Draw a straight horizontal ground line across the bottom of the diagram. The ground line passes through the origin.
- On the y-axis, place a clearly labeled height mark at "2.0 m" above the ground.
- From that 2.0 m mark, draw a thin dashed horizontal line extending rightward to indicate the launch height.

Student and launch point:
- Place the student (simple stick figure) on the left side of the y-axis, standing on the ground line.
- The student’s throwing hand is located exactly on the dashed horizontal line labeled "2.0 m" (this point is the launch point).
- At the launch point, draw a small solid circle (the ball at t = 0).

Initial velocity vector of the ball:
- From the ball at the launch point, draw a single bold arrow representing the initial velocity vector.
- The arrow must point up and to the right, making an angle of exactly "53°" measured counterclockwise from the +x direction.
- Place a small angle arc at the tail of the velocity vector between the +x direction and the vector, labeled "53°".
- Label the velocity vector with the visible text "v₀ = 15 m/s" placed alongside the arrow.

Building and elevator:
- Draw a tall rectangular building on the right half of the diagram, separated from the student by open air (no overlap).
- The building’s base sits on the same ground line as the origin.
- Inside the building, draw a vertical elevator shaft as two parallel vertical lines.
- Draw an elevator car as a rectangle within the shaft, positioned in the lower half of the building.
- On the elevator car, draw a small stick figure (person in elevator) facing left toward a window.
- Draw a rectangular window on the left wall of the elevator shaft aligned with the person’s head/torso so they can "observe" outward.

Elevator motion indicator:
- Next to the elevator car, draw a bold vertical arrow pointing straight downward.
- Label this arrow with the visible text "v_elevator = 3.0 m/s downward".

Overall spatial relationships (must be visually unambiguous):
- The student and launch point are left of the building.
- The velocity vector points toward the building side (rightward component).
- The building is entirely to the right of the y-axis and does not cover the axes.

Style:
- Use clean black line art on a white background.
- All numeric values shown must exactly match: 2.0 m, 15 m/s, 53°, 3.0 m/s.
- No additional numbers or extraneous labels.

Figure 2. Axes for drawing the initial velocity vector and its components.

Vector-diagram axes intended for student drawings, with an unambiguous scale and labeling.

Axes:
- Draw a horizontal axis with arrowhead on the positive (right) end, labeled "x" near the arrow.
- Draw a vertical axis with arrowhead on the positive (up) end, labeled "y" near the arrow.
- The axes intersect at a single origin point.
- Label the origin with the visible text "0".

Grid:
- Add a light square grid covering the full plotting area.
- Grid spacing corresponds to 1 unit per small square (units are not written on the grid).

Reference scale for vector length (must be shown so proportionality is possible):
- Near the bottom edge, include a small horizontal reference arrow (a scale bar) labeled "5 m/s".
- The reference arrow length equals exactly 5 grid squares.

No pre-drawn vectors:
- Do not draw any velocity vectors or components; leave the axes otherwise blank for student work.

Style:
- Black axes, light gray grid, white background.
- No title beyond the caption; no extra numeric markings on the axes besides the origin label "0" and the scale bar label "5 m/s".

On the coordinate axes in Figure 2, draw a vector to represent the initial velocity of the ball as observed by the student on the ground. The length of the vector should be proportional to the magnitude of the velocity. On the same axes, draw the horizontal and vertical components of the initial velocity vector. Label each component with its magnitude.

Derive an expression for the vertical component of the ball's velocity as measured by the person in the elevator at time $t$ after the ball is thrown. Express your answer in terms of the given quantities (initial speed $v_0 = 15$ m/s, angle $\theta = 53°$ , elevator speed $v_{elevator} = 3.0$ m/s), $t$ , $g$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The person in the elevator observes the ball's motion from the elevator reference frame.

Figure 3. Axes for v_y of the ball vs time as measured by the student on the ground.

Blank graph axes for plotting the vertical velocity component v_y versus time t (ground frame).

Axes (REQUIRED, with exact numeric ticks):
- Horizontal axis label: "t (s)".
- Horizontal axis range: from 0 to 4.
- Horizontal tick marks: every 1 s.
- Horizontal tick labels visible: "0, 1, 2, 3, 4".
- Vertical axis label: "v_y (m/s)".
- Vertical axis range: from −15 to +15.
- Vertical tick marks: every 5 m/s.
- Vertical tick labels visible: "−15, −10, −5, 0, 5, 10, 15".
- The origin is the intersection of the axes and is labeled "0".
- Arrowheads appear on the positive ends of both axes (right end of t-axis, top end of v_y-axis).

No curve pre-drawn:
- Do not draw the v_y(t) line; leave the plotting region blank.

End-of-flight instruction cue (visual, non-numeric):
- Add a small note near the right side of the plotting area reading "end when ball reaches ground" with a thin pointer line aimed toward the right edge of the time axis (no specific time marked).

Style:
- Clean black axes on white background.
- No grid lines.
- No additional annotations beyond axis labels, tick labels, origin label, and the end-of-flight note.

On the axes in Figure 3, sketch a graph of the vertical component of velocity $v_y$ of the ball as a function of time $t$ as measured by the student on the ground. The graph should begin at $t = 0$ when the ball is thrown and end when the ball reaches the ground. Clearly indicate the initial value of $v_y$ and any intercepts with numerical values or expressions. Consider the motion of the ball as observed by the student on the ground.

Figure 4. Axes for v_y of the ball vs time as measured by a person in the descending elevator.

Blank graph axes for plotting the vertical velocity component v_y versus time t (elevator frame). Use the exact same axis scaling as Figure 3.

Axes (REQUIRED, with exact numeric ticks):
- Horizontal axis label: "t (s)".
- Horizontal axis range: from 0 to 4.
- Horizontal tick marks: every 1 s.
- Horizontal tick labels visible: "0, 1, 2, 3, 4".
- Vertical axis label: "v_y (m/s)".
- Vertical axis range: from −15 to +15.
- Vertical tick marks: every 5 m/s.
- Vertical tick labels visible: "−15, −10, −5, 0, 5, 10, 15".
- The origin is the intersection of the axes and is labeled "0".
- Arrowheads appear on the positive ends of both axes (right end of t-axis, top end of v_y-axis).

No curve pre-drawn:
- Do not draw the v_y(t) line; leave the plotting region blank.

End-of-flight instruction cue (visual, non-numeric):
- Add the same small note near the right side of the plotting area reading "same time interval as Fig. 3" and another note reading "end when ball reaches ground" (no specific time marked).

Style:
- Clean black axes on white background.
- No grid lines.
- No additional annotations beyond axis labels, tick labels, and the two notes.

On the axes in Figure 4, sketch a graph of the vertical component of velocity $v_y$ of the ball as a function of time $t$ as measured by the person in the elevator. Use the same time interval as in Part C. Now consider the motion of the ball as observed by the person in the elevator moving downward at constant velocity $v_{elevator} = 3.0$ m/s.

Describe one specific quantitative feature of the graph in Figure 4 that differs from the graph in Figure 3. State explicitly what the feature is and whether it increases or decreases compared to Figure 3.

Briefly justify your answer using physics principles.