AP Physics 1 FRQ Practice

Practice FRQ 1 of 20

1. A student stands on a walkway that moves at a constant speed to the east. At time

t=0

the student throws a ball from point

P

on the walkway, as shown in Figure 1. Air resistance is negligible, and the ball's motion after release is influenced only by gravity.

Figure 1. Ball thrown from a moving walkway: ground x–y axes, walkway motion east at speed v_w, and initial throw velocity relative to the walkway v₀ at angle θ.

$Create a clean, black-and-white physics setup diagram with no background scenery. Overall layout and coordinate system: - Draw a pair of perpendicular coordinate axes near the left side of the diagram. - The horizontal axis is labeled "+x (east)" with an arrowhead on its right end. - The vertical axis is labeled "+y" with an arrowhead on its top end. - The axes intersect at a single point that represents the origin; label this intersection with the visible text "0". Moving walkway: - Draw the moving walkway as a long, thick, horizontal rectangular platform spanning most of the width of the figure. - The top surface of the walkway is a straight horizontal line; the walkway is centered vertically in the lower half of the diagram. - The walkway’s top surface is parallel to the +x axis. - Place a bold rightward arrow directly above the walkway (centered horizontally on the walkway) to indicate walkway motion. - Label this arrow exactly with the text "v_w" placed just above the arrow’s midpoint. Point P (release point) and student: - Mark a single point on the top surface of the walkway in the left half of the walkway (clearly not at an edge). This is the release point. - Label the point with the visible text "P" placed just above and slightly left of the point so it does not overlap the point. - Draw a simple student figure (stick figure or minimal silhouette) standing on the walkway with feet on the top surface, positioned so that one hand is directly above point P. Ball at release: - Draw a small filled circle (the ball) at the student’s hand location directly above point P, indicating the ball at the instant of release. Initial velocity relative to the walkway: - From the ball, draw a straight arrow representing the ball’s initial velocity relative to the walkway. - The arrow must point up and to the right (first quadrant), making an acute angle with the horizontal. - Place the label "\vec v_{0,\text{walk}}" along the arrow, centered and slightly offset so the text does not sit on top of the arrow line. Angle θ definition: - At the ball (tail of the velocity arrow), draw a small angle arc between a horizontal reference line and the velocity arrow. - The horizontal reference line for the angle is a short dashed or thin solid line extending to the right from the ball, parallel to the walkway surface and parallel to the +x axis. - The angle arc opens from the horizontal reference line up to the velocity arrow, clearly indicating the angle above horizontal. - Label the arc with the Greek letter "θ" placed just outside the arc. Consistency requirements: - Ensure the velocity arrow is clearly drawn relative to the walkway (not relative to vertical). - Ensure the walkway motion arrow labeled v_w is purely horizontal to the right. - Do not add any numerical values that are not given; only show the symbols v_w, P, \vec v_{0,\text{walk}}, θ, and the axis labels +x (east) and +y.$

Figure 2. Axes for a graph of the y-component of velocity v_y versus time t, with labeled times 0, t₁, and t₂.

Create a blank set of graph axes (no curve), black lines on a white background, with light gray grid lines.

Axes formatting:
- Horizontal axis label: "t (s)" centered below the axis.
- Vertical axis label: "v_y (m/s)" centered along the vertical axis, rotated to read bottom-to-top.
- Place arrowheads on the positive (right) end of the t-axis and the positive (top) end of the v_y-axis.
- The axes intersect at the origin in the lower-left quadrant of the plotting area; label the origin with the visible text "0" at the intersection.

X-axis (time) numerical scale and ticks:
- The x-axis begins at the origin and extends to the right edge.
- Show three labeled tick marks on the x-axis:
- The first tick at the origin is labeled "0".
- A second tick to the right is labeled "t₁".
- A third tick farther right is labeled "t₂".
- Enforce the spacing relationship: the tick labeled "t₁" is exactly halfway between the tick labeled "0" and the tick labeled "t₂".
- Extend the x-axis beyond the tick labeled "t₂" by an additional visible segment equal in length to at least one-half of the 0-to-t₂ distance, so the axis clearly includes times greater than t₂ (no additional tick labels are required in that region).

Y-axis (vertical velocity) scale and ticks:
- The y-axis passes through the origin and extends upward and downward.
- Include evenly spaced tick marks above and below the origin, but do not assign any numeric values to these ticks (since v_y values are to be labeled in terms of symbols in the student response).
- Ensure there are at least three tick intervals above the origin and at least three tick intervals below the origin so both positive and negative v_y can be plotted.

Grid:
- Add faint, evenly spaced grid lines: vertical grid lines aligned with the x-axis tick marks (including those at 0, t₁, t₂) and additional evenly spaced vertical lines between them.
- Add faint, evenly spaced horizontal grid lines aligned with the y-axis tick marks.

No plotted data:
- Do not draw any curve or points.
- Do not include any title beyond the caption.
- Do not include any extra labels besides: "t (s)", "v_y (m/s)", "0", "t₁", and "t₂".

i. On the axes shown in Figure 2, sketch a graph of the y-component of the ball's velocity

v_y

as a function of time

t

from

t=0

until

t>t_2

. Label the values of

v_y

t=0

t=t_1

, and

t=t_2

in terms of

v_0

\theta

, and physical constants, as appropriate.

ii. Derive an expression for the time interval

t_2

from when the ball is thrown until it returns to the release height, as measured by an observer at rest with the ground. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Express your final answer in terms of

v_0

\theta

, and

g

iii. Derive an expression for the x-component of the ball's displacement

\Delta x_{\text{ground}}

from

t=0

t=t_2

, as measured by an observer at rest with the ground. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Express your final answer in terms of

v_0

\theta

v_w

, and

g

B. Indicate whether the magnitude of the ball's average velocity over the interval

0

t_2

is greater for Observer G, greater for Observer W, or the same for both observers.
______ Greater for Observer G
______ Greater for Observer W
______ The same for both observers
Justify your response.

Practice FRQ 1 of 20

1. A student stands on a walkway that moves at a constant speed to the east. At time

t=0

the student throws a ball from point

P

on the walkway, as shown in Figure 1. Air resistance is negligible, and the ball's motion after release is influenced only by gravity.

Figure 1. Ball thrown from a moving walkway: ground x–y axes, walkway motion east at speed v_w, and initial throw velocity relative to the walkway v₀ at angle θ.

Figure 2. Axes for a graph of the y-component of velocity v_y versus time t, with labeled times 0, t₁, and t₂.

i. On the axes shown in Figure 2, sketch a graph of the y-component of the ball's velocity

v_y

as a function of time

t

from

t=0

until

t>t_2

. Label the values of

v_y

t=0

t=t_1

, and

t=t_2

in terms of

v_0

\theta

, and physical constants, as appropriate.

ii. Derive an expression for the time interval

t_2

v_0

\theta

, and

g

iii. Derive an expression for the x-component of the ball's displacement

\Delta x_{\text{ground}}

from

t=0

t=t_2

v_0

\theta

v_w

, and

g

B. Indicate whether the magnitude of the ball's average velocity over the interval

0

t_2