AP Physics 1 FRQ Practice

🎡AP Physics 1

Practice FRQ 1 of 201/20

1. A student rolls a cart along a straight, horizontal track. At the same instant the cart passes a launch point, a ball is launched from the cart and moves in the plane of the floor, as shown in Figure 1. Air resistance is negligible.

Figure 1. Cart moving along a horizontal track; at the instant the cart passes the launch point (t = 0), a ball is launched from the cart with initial velocity relative to the cart.

$A clean physics schematic (no 3D perspective), drawn as a SIDE VIEW in the x–y plane. FRAME AND REFERENCE DIRECTIONS: - The diagram is a wide horizontal rectangle. - A coordinate axis symbol is drawn near the left side of the figure, above the track: a horizontal arrow labeled “+x” pointing to the right, and a vertical arrow labeled “+y” pointing upward. The axes share a single common origin point (a small dot) at their intersection. TRACK (FLOOR/RAIL): - A single straight horizontal line representing the track/floor runs left-to-right across the lower quarter of the diagram. - The track line is perfectly level (no slope) and unbroken. LAUNCH POINT (ON THE TRACK): - On the track line, place a distinct vertical tick mark at the horizontal midpoint of the entire figure. - Directly above this tick mark, place the text label “launch point”. - This launch-point tick mark is the only special marker on the track. CART: - A cart is drawn centered horizontally so that its midpoint is directly above the launch-point tick mark (meaning: the cart is shown at the exact instant it passes the launch point). - The cart body is a low rectangle resting on two wheels that touch the track line. - The cart’s length is visually large (spanning roughly one-fifth to one-quarter of the full figure width) and its height is smaller (roughly one-third of its own length). - Two identical circular wheels are drawn under the cart body, one near the left end and one near the right end of the cart body; both wheels rest on the track line. CART VELOCITY VECTOR (GROUND FRAME): - From the cart body, draw a bold horizontal arrow pointing to the right. - Place the label “$\vec{v}_c$” directly above the shaft of this rightward arrow. - The arrow must be perfectly horizontal (parallel to the track) to emphasize motion purely along +x. BALL AT THE INSTANT OF LAUNCH: - A small filled circle (the ball) is drawn just above the top surface of the cart, vertically aligned with the cart’s center. - The ball is shown at the instant of launch, so it is not drawn along a trajectory; it appears only at the launch location above the cart. BALL’S INITIAL VELOCITY RELATIVE TO THE CART: - Starting at the center of the ball, draw a bold vertical arrow pointing straight upward (parallel to +y). - Label this arrow “$\vec{v}_{b/c,0}$” placed to the right side of the arrow, centered vertically along the arrow’s length. - The arrow must be perfectly vertical to indicate “straight upward relative to the cart.” CLARITY/STYLE REQUIREMENTS: - No additional forces are drawn (no gravity arrow) and no trajectory curve is drawn. - All labels are printed clearly and do not overlap the cart, ball, or axes. - Only these visible text items appear: “+x”, “+y”, “launch point”, “$\vec{v}_c$”, and “$\vec{v}_{b/c,0}$”$

Figure 2. Axes for plotting the ball’s vertical velocity component $v_y$ versus time $t$ from $t=0$ to $t=t_1$.

$A blank Cartesian graph with grid lines. AXES (with arrows and numeric scales): - Horizontal axis: labeled “$t$ (s)” centered below the axis. The axis starts at 0 on the left and ends at $t_1$ on the right. - Vertical axis: labeled “$v_y$ (m/s)” centered along the vertical axis. The vertical axis has a positive direction upward and negative direction downward. - The axes intersect at the origin, and the origin is explicitly labeled with the visible text “0” at the intersection. - Both axes have arrowheads only on their positive ends (right end for time, top end for $v_y$). X-AXIS TICK MARKS (exact): - The left end tick is labeled “0”. - The right end tick is labeled “$t_1$”. - Exactly four equally spaced interior tick marks appear between 0 and $t_1$, creating five equal time intervals across the width. - None of the interior x-axis ticks have numeric labels; only “0” and “$t_1$” are labeled. Y-AXIS TICK MARKS (exact): - The y-axis shows a symmetric scale about zero: equal vertical extent above and below the origin. - There are exactly three equally spaced tick marks above the origin and three equally spaced tick marks below the origin. - The tick mark at the origin corresponds to $v_y=0$ (unlabeled except for the origin label “0” at the axes intersection). - No additional numeric labels appear on the y-axis besides the origin label “0”. GRID LINES (exact count and spacing): - Light gray grid lines fill the plotting area. - Vertical grid lines align with every x-axis tick mark (including 0 and $t_1$), producing a total of six vertical grid lines across the plotting region. - Horizontal grid lines align with every y-axis tick mark (including the origin), producing a total of seven horizontal grid lines. NO CURVE DRAWN: - The plotting area contains no data points, no curve, and no annotations other than axis labels and the tick labels “0” and “$t_1$”.$

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

v_y

as a function of time

t

from

t=0

until

t=t_1

ii. Derive an expression for the time

t_1

when the ball returns to the launch height in terms of

v_{b/c,0y}

and

g

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii. Derive an expression for the ball's horizontal displacement

\Delta x

in the ground frame from

t=0

t=t_1

in terms of

v_{c}

v_{b/c,0x}

v_{b/c,0y}

, and

g

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

An observer on the cart measures the ball's motion during the flight. Assume the cart is an inertial reference frame because it moves with constant velocity relative to the ground.

B. Indicate whether the x-component of the ball's velocity as measured by the observer on the cart increases, decreases, or remains constant during the time interval

0<t<t_1

.
______ Increases
______ Decreases
______ Remains constant
Justify your response.

🎡AP Physics 1

Practice FRQ 1 of 201/20

Figure 1. Cart moving along a horizontal track; at the instant the cart passes the launch point (t = 0), a ball is launched from the cart with initial velocity relative to the cart.

Figure 2. Axes for plotting the ball’s vertical velocity component $v_y$ versus time $t$ from $t=0$ to $t=t_1$.

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

v_y

as a function of time

t

from

t=0

until

t=t_1

ii. Derive an expression for the time

t_1

when the ball returns to the launch height in terms of

v_{b/c,0y}

and

g

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii. Derive an expression for the ball's horizontal displacement

\Delta x

in the ground frame from

t=0

t=t_1

in terms of

v_{c}

v_{b/c,0x}

v_{b/c,0y}

, and

g

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

An observer on the cart measures the ball's motion during the flight. Assume the cart is an inertial reference frame because it moves with constant velocity relative to the ground.

B. Indicate whether the x-component of the ball's velocity as measured by the observer on the cart increases, decreases, or remains constant during the time interval

0<t<t_1

.
______ Increases
______ Decreases
______ Remains constant
Justify your response.