AP Physics C: Mechanics FRQ practice

The horizontal components of the ball's velocity as measured by Observer A and Observer B are $v_{xA}$ and $v_{xB}$, respectively, during the time the ball is in the air.

Derive an expression for the horizontal distance $x$ that the ball travels from the launch point until it returns to the height of the truck bed as measured by Observer A. Express your answer in terms of $v_0$, $u_0$, $g$, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the motion of the ball as measured by Observer A in the ground reference frame. Use the coordinate system shown in Figure 2, where the origin is at ground level directly below the launch point at $t = 0$. The truck bed is at height $y_0$ above the ground.

Indicate whether the time for the ball to return to the height of the truck bed as measured by Observer A is greater than, less than, or equal to the time measured in the original scenario where the truck moved with constant velocity. In a different scenario, the truck now accelerates with constant acceleration $a_0$ to the right along the horizontal road. At time $t = 0$, when the truck has instantaneous velocity $v_0$, the ball is again launched vertically upward from the truck bed with initial speed $u_0$ relative to the truck.