AP Physics 1 FRQ Practice

🎡AP Physics 1

Practice FRQ 1 of 201/20

4. In Scenario 1, a student stands on the ground and observes a cart moving to the right at a constant speed $v_c = 4.0\ \text{m/s}$ on a horizontal track, as shown in Figure 1. At the instant the cart passes the student, a ball is thrown straight upward from the cart with an initial speed (relative to the cart) of $v_{y0} = 8.0\ \text{m/s}$ . The ball is released from a height $y_0 = 1.2\ \text{m}$ above the ground. Air resistance is negligible and the acceleration due to gravity is $g = 9.8\ \text{m/s}^2$ downward. The student measures the ball's initial velocity components as $v_{x1}$ and $v_{y1}$ and the ball's average velocity over the first $\Delta t = 0.50\ \text{s}$ as $\vec{v}_{\text{avg}1}$ .

In Scenario 2, a second student rides on the cart and is at rest with respect to the cart. At the same instant described in Scenario 1, the second student observes the same ball being thrown straight upward from the cart with initial speed (relative to the cart) $v_{y0} = 8.0\ \text{m/s}$ from height $y_0 = 1.2\ \text{m}$ . Air resistance is negligible and the acceleration due to gravity is $g = 9.8\ \text{m/s}^2$ downward. The second student measures the ball's initial velocity components as $v_{x2}$ and $v_{y2}$ and the ball's average velocity over the first $\Delta t = 0.50\ \text{s}$ as $\vec{v}_{\text{avg}2}$ .

Figure 1. Cart moving right at constant speed as a ball is thrown straight upward from the cart at the instant the cart passes a stationary student. The release height is y0 = 1.2 m above the ground, with axes +x right and +y up.

Refer to Figure 1. Let $v_{x1}$ be the horizontal component of the ball's initial velocity as measured by the stationary ground-frame observer (the student), and let $v_{x2}$ be the horizontal component of the ball's initial velocity as measured by an observer riding on the cart. Indicate whether $v_{x1}$ is greater than, less than, or equal to $v_{x2}$ by writing one of the following in your answer booklet.

• $v_{x1} > v_{x2}$
• $v_{x1} < v_{x2}$
• $v_{x1} = v_{x2}$

Justify your answer in terms of the reference frame of each observer and the vector addition of velocities in one dimension. Use qualitative reasoning beyond referencing equations.

Starting with a fundamental kinematics principle for relative motion (Galilean transformation), derive expressions for the ground-frame initial velocity components $v_{x1}$ and $v_{y1}$ of the ball. Express your answers in terms of $v_c$ and $v_{y0}$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the general case of a cart moving at constant speed $v_c$ in the $+x$ direction while a ball is thrown straight upward relative to the cart with initial vertical speed $v_{y0}$ . Ignore air resistance. Take $+y$ upward and acceleration due to gravity as $\vec{a} = -g\,\hat{j}$ .

Indicate whether the expressions you derived in part B are or are not consistent with the comparison made in part A. Briefly justify your answer by referencing your expressions from part B and explaining how changing the observer's inertial reference frame changes (or does not change) the measured horizontal component of velocity.