On Figure 2, draw an arrow to represent the velocity vector of the ball at $t = 0$ as observed in Frame S (the student's reference frame). On Figure 3, draw an arrow to represent the velocity vector of the ball at $t = 0$ as observed in Frame G (the ground reference frame). The length and direction of each arrow should accurately represent the magnitude and direction of the velocity vector in each reference frame. Label each arrow with its magnitude in m/s.

Derive an expression for the horizontal distance $\Delta x$ traveled by the ball, as measured in Frame G, from the moment it is released until it hits the ground. Express your answer in terms of $v_0$, $u_0$, $h$, $g$, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The ball reaches its maximum height and then falls to the ground.

On the axes in Figure 4, sketch a graph of the vertical component of the velocity $v_y$ of the ball as a function of time $t$ in Frame G, from $t = 0$ until the ball hits the ground. Clearly indicate the initial value and any intercepts with the axes. The vertical component of the ball's velocity is analyzed as a function of time in Frame G.

Describe one feature of the graph of the magnitude of the ball's acceleration $|\vec{a}|$ as a function of time in Frame G, from $t = 0$ until the ball hits the ground. Specifically state whether this magnitude increases, decreases, or remains constant. A second student on the ground at position $x = 0$ observes the ball's motion and records the ball's position vector as a function of time in Frame G. The position vector can be written as $\vec{r}(t) = x(t)\hat{i} + y(t)\hat{j}$, where $x(t)$ and $y(t)$ are the horizontal and vertical components of position.