On the axes in Figure 2, sketch a graph of the vertical component of the ball's velocity $v_y$ as a function of time $t$ for the entire flight from $t = 0$ to $t = 1.2$ s. The graph should show correct initial and final values, and the value at maximum height.

Derive an expression for the magnitude of the ball's displacement from its launch point to its position at $t = 0.30$ s. Express your answer in terms of $x_1$, $y_1$, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Calculate a numerical value for the displacement. At time $t = 0.30$ s, the ball is at position $(x_1, y_1)$ where $x_1 = 2.4$ m and $y_1 = 1.35$ m.

On the coordinate system in Figure 3, draw and label two vectors: At time $t = 0.90$ s, the ball is descending toward the ground.

Describe how one component of the ball's velocity as measured by the observer on the cart differs from that component as measured by an observer on the ground. Specify which component (horizontal or vertical) you are describing and state whether its magnitude is greater than, less than, or equal to the magnitude measured from the ground. An observer stands on a cart that moves to the right with a constant velocity of $v_{cart} = 6.0$ m/s, as shown in Figure 4. The cart begins moving at $t = 0$, at the same instant the ball is launched. The ball is launched from a position directly beside the cart.