The horizontal component of the ball's velocity as measured by the student on the platform is $v_{x,p}$, and the horizontal component of the ball's velocity as measured by the stationary observer on the ground is $v_{x,g}$.

Derive an expression for the horizontal distance $d$ traveled by the object before it hits the ground. Express your answer in terms of $v_{0x}$, $v_{0y}$, $h$, $g$, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider a general case where an object is thrown with initial velocity components $v_{0x}$ and $v_{0y}$ (relative to the ground) from a height $h$ above the ground.

Indicate whether the time the ball remains in the air in this new scenario is greater than, less than, or equal to the time the ball remains in the air in the original scenario. Use Figure 2 to sketch the vertical velocity component as a function of time for this new scenario. In a different scenario, the platform moves with the same speed $v_p = 3.0 \text{ m/s}$ to the right, but the student now throws the ball with the same initial speed $v_0 = 8.0 \text{ m/s}$ relative to the platform at an angle $\theta = 60°$ backward (toward the left) and upward. The ball is released from a height of $h = 1.2 \text{ m}$ above the ground in both the original scenario and this new scenario.