AP Physics C: Mechanics FRQ Practice

⚙️AP Physics C: Mechanics

Guided Practice

Practice FRQ 1 of 81/8

1. A drone is programmed to fly horizontally at constant altitude in a region where air resistance is negligible. At time t = 0, the drone is at position x = 0, y = 0 and has velocity components vx = 15 m/s and vy = 0 m/s in the coordinate system shown in Figure 1. At t = 0, the drone releases a package. The package falls freely under the influence of gravity while the drone continues its horizontal motion. Use g = 10 m/s² for the magnitude of the acceleration due to gravity.

Figure 1: Coordinate system and initial velocity of the drone (and released package) at t = 0

A clean, black-and-white physics diagram showing an x–y coordinate system with the origin clearly identified.

Axes and origin:
- Draw two perpendicular axes crossing at the origin.
- Horizontal axis labeled "x" with an arrowhead on the positive end pointing to the right.
- Vertical axis labeled "y" with an arrowhead on the positive end pointing upward.
- Place the text "(0, 0)" immediately adjacent to the origin point (slightly below-left of the intersection) so it is unambiguous that the origin is the position x = 0, y = 0 at t = 0.

Drone and package at the instant of release:
- Draw a small drone icon (simple outline: a small central body with two short rotor arms) centered exactly on the origin so the drone’s position at t = 0 is unambiguous.
- Draw a small square or small box icon representing the package directly beneath the drone body, touching the drone (visually indicating it is being carried at that instant). The package must be vertically aligned with the origin (same horizontal position as the drone).
- Add a short label "package" with a thin leader line pointing to the small box.
- Add a short label "drone" with a thin leader line pointing to the drone body.

Initial velocity vector (horizontal only):
- From the origin, draw a single velocity arrow exactly along the +x axis (perfectly horizontal, no upward or downward tilt).
- The arrow tail begins at the origin and the arrowhead points right.
- Label the arrow above it with the text "vₓ = 15 m/s".
- Also include the text "vᵧ = 0" near the origin (placed slightly above the origin), making explicit that the initial vertical velocity component is zero.

Style constraints:
- Use solid black lines; medium line weight for axes and the velocity arrow.
- No grid, no numeric tick marks on the axes in this figure.
- Keep the diagram uncluttered: only the axes labels (x, y), the origin label (0, 0), the drone/package labels, and the velocity component labels (vₓ = 15 m/s and vᵧ = 0).

Figure 2: Velocity-component grid for drawing the package velocity vector at t = 2.0 s

A square coordinate grid intended for drawing a velocity vector, with clearly numbered tick marks and axis labels.

Overall layout:
- The grid occupies most of the figure area and is centered.
- Use light gray grid lines and darker black axes.

Horizontal axis (vₓ):
- The horizontal axis runs through the middle of the grid and is labeled "vₓ (m/s)" near the positive (right) end.
- The axis has an arrowhead on the positive (right) end.
- Numeric range shown on the axis: from 0 at the origin to 20 at the far right end.
- Tick marks and labels appear at 0, 5, 10, 15, and 20.
- Ensure that each of these numbers (0, 5, 10, 15, 20) is printed directly below the corresponding tick mark.

Vertical axis (vᵧ):
- The vertical axis runs through the origin and is labeled "vᵧ (m/s)" near the positive (top) end.
- The axis has an arrowhead on the positive (top) end.
- Numeric range shown on the axis: from +5 at the top down to −25 at the bottom.
- Tick marks and labels appear at +5, 0, −5, −10, −15, −20, and −25.
- Ensure that each of these numbers (+5, 0, −5, −10, −15, −20, −25) is printed to the left of the corresponding tick mark.

Origin:
- The origin is the intersection of the vₓ and vᵧ axes and must be explicitly labeled with the number "0" on both axes (i.e., the 0 tick label on the horizontal axis at the intersection and the 0 tick label on the vertical axis at the intersection).
- Additionally, place a small solid dot at the origin to emphasize where the arrow must start.

Grid spacing consistency:
- The spacing between adjacent labeled ticks corresponds to 5 m/s in both directions.
- All grid squares are uniform; vertical spacing from 0 to +5 is the same as from 0 to −5, etc.

Drawing instruction compatibility:
- Do not pre-draw any velocity vector arrow in this figure.
- The figure must make it easy for a student to draw an arrow starting at the origin with components readable against the tick marks.

Style constraints:
- Black text for all labels and numbers.
- Light gray grid lines at every 5 m/s increment, extending across the full grid in both directions.
- No additional titles inside the grid beyond axis labels and tick values.

i. On the grid in Figure 2, draw an arrow to represent the velocity vector of the package at time t = 2.0 s as measured in the coordinate system shown in Figure 1.

• The arrow should start at the origin of the grid.

• The length of the arrow components should be proportional to the velocity components vx and vy.

ii. Derive an expression for the y-component of the position of the package as a function of time t. Express your answer in terms of t, g, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

An observer on the ground watches the package fall and measures its motion in the coordinate system shown in Figure 1. A second observer in a car drives horizontally at constant speed vc = 15 m/s in the +x-direction and also watches the package fall, measuring its motion in a reference frame moving with the car.

B. Derive an expression for the magnitude of the velocity of the package at time t = 2.0 s as measured by the observer in the car. Express your answer in terms of g and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.