AP Physics 1 FRQ Practice

🎡AP Physics 1

Practice FRQ 1 of 171/17

1. A rescue boat travels on a straight river where the water flows east at a constant speed of 2.0 m/s relative to the riverbank. At time t = 0, the boat is at position (x, y) = (0 m, 0 m) as measured from the riverbank reference frame, where +x is east and +y is north. The boat's motor maintains a constant speed of 6.0 m/s relative to the water and is aimed 30° west of north, as shown in Figure 1.

Figure 1. Velocity vectors for a rescue boat and flowing river, shown in the riverbank reference frame.

A clean physics vector diagram on a white background.

Coordinate system and origin:
- Draw a bold set of perpendicular axes crossing at the boat’s starting point.
- Label the intersection with visible text: "(0 m, 0 m)".
- Horizontal axis: arrow pointing to the right; label near the arrowhead: "+x (east)".
- Vertical axis: arrow pointing upward; label near the arrowhead: "+y (north)".

Boat at start:
- Place a small solid dot exactly at the axes intersection to represent the boat at t = 0.
- Label it "boat" with a short leader line pointing to the dot.

North bank line:
- Draw a perfectly straight horizontal line representing the north bank across the entire width of the diagram, positioned well above the origin so the origin is clearly below it.
- Place the line perpendicular to the +y axis (so it is flat/level).
- Label this line "north bank" centered above the line.
- Add a vertical distance annotation from the origin straight upward to the bank line: a thin vertical bracket or double-headed arrow aligned with the +y axis.
- Next to that vertical distance marker, place the text "48 m".
- Also place the equation-style label "y = 48 m" adjacent to the bank line (slightly above or on the line), making clear that the bank corresponds to that y-value.

Water velocity vector (water relative to riverbank):
- From the origin, draw a solid arrow strictly along the +x direction (perfectly horizontal to the right).
- Place the label along or just above this arrow: "v_water,bank = 2.0 m/s".
- Ensure the arrow direction is unambiguously east (rightward) with no vertical component.

Boat motor velocity vector (boat relative to water):
- From the origin, draw a second solid arrow pointing generally upward but tilted to the left of the +y axis.
- The arrow must make an angle of exactly 30° measured from the +y axis toward the −x direction (i.e., 30° west of north).
- Show this angle explicitly: draw a small curved angle arc at the origin between the +y axis and this boat-relative-to-water arrow on the left side of the +y axis.
- Label the angle arc with visible text "30°".
- Label the arrow itself (placed along the arrow or just beside it): "v_boat,water = 6.0 m/s".

Vector styling and clarity rules:
- Both velocity vectors originate exactly at the origin dot.
- Use medium-thick black arrows; arrowheads clearly visible.
- Keep labels readable and not overlapping.
- No extra vectors, no trajectory curve, and no additional numeric values besides 2.0 m/s, 6.0 m/s, 30°, (0 m, 0 m), 48 m, and y = 48 m.

Figure 2. Axes for graphing the y-component of the boat’s velocity v_y versus time t (riverbank frame).

A blank set of graph axes (no curve drawn) on a white background with light gray grid lines.

Axes and labels:
- Horizontal axis: labeled "t (s)" centered beneath the axis.
- Vertical axis: labeled "v_y (m/s)" centered along the vertical axis.
- Place arrows on the positive ends of both axes (right end of t-axis and top end of v_y-axis).
- The origin at the axes intersection is labeled with the visible tick label "0" on both axes (a single "0" at the intersection is acceptable if it clearly marks the origin).

X-axis (time) numeric scale (must be explicit):
- The time axis runs from 0 s at the origin to 12 s at the far right edge.
- Tick marks every 2 s, labeled: 0, 2, 4, 6, 8, 10, 12.
- In addition to the numeric ticks, include two special labeled tick marks:
- A tick labeled "t₁" placed exactly at 8 s.
- A tick labeled "t₂" placed exactly at 10 s.
- The labels "t₁" and "t₂" should appear directly under their respective tick marks and be distinct from the numeric tick labels.

Y-axis (vertical velocity component) numeric scale:
- The vertical axis runs from 0 m/s at the origin to 6 m/s at the top edge.
- Tick marks every 1 m/s, labeled: 0, 1, 2, 3, 4, 5, 6.

Grid lines:
- Show faint vertical grid lines aligned with each 2 s tick.
- Show faint horizontal grid lines aligned with each 1 m/s tick.

No plotted data:
- Do not draw any curve, line, point markers, or shaded region.
- The only visible text on the graph is the axis labels, numeric tick labels, and the special tick labels "t₁" and "t₂".

On the axes shown in Figure 2, sketch a graph of the y-component of the boat's velocity $v_y$ as a function of time $t$ from $t = 0$ until $t > t_2$ as measured in the riverbank reference frame.

ii.

Derive an expression for the boat's velocity components $v_x$ and $v_y$ in the riverbank reference frame in terms of the given speeds and the angle $30^\circ$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii.

Derive an expression for the boat's x-position $x(t_1)$ when it reaches the north bank at $y = 48\ \text{m}$ . Express your answer in terms of the given quantities and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Indicate whether the x-component of the boat's velocity measured by this drifting observer is positive, negative, or zero. Consider an observer in a second inertial reference frame that moves east at a constant speed of 2.0 m/s relative to the riverbank (the observer drifts with the current).

Positive
Negative
Zero
Justify your response.