fabrizio

1. As you look out of your dorm window, a flower pot suddenly falls past. The pot is visible for a time t, and the vertical length of your window is L_w. Take down to be the positive direction, so that downward velocities are positive and the acceleration due to gravity is the positive quantity g.

Assume that the flower pot was dropped by someone on the floor above you (rather than thrown downward).

From what height h above the bottom of your window was the flower pot dropped? Express the answer in terms of L_w, t, and g.

2. Two basketball players are essentially equal in all respects. (They are the same height, they jump with the same initial velocity, etc.) In particular, by jumping they can raise their centers of mass the same vertical distance, H (called their "vertical leap"). The first player, Arabella, wishes to shoot over the second player, Boris, and for this she needs to be as high above Boris as possible. Arabella jumps at time t=0, and Boris jumps later, at time t_R (his reaction time). Assume that Arabella has not yet reached her maximum height when Boris jumps.

Find the vertical displacement D(t) = h_A(t) - h_B(t), as a function of time for the interval 0 < t < t_R, where h_A(t) is the height of the raised hands of Arabella, while h_B(t) is the height of the raised hands of Boris.