Two basketball players are essentially equal in all respects.(They are the same height, they jump with the same initialvelocity, etc.) In particular, by jumping they can raise theircenters of mass the same vertical distance, H (called their "vertical leap"). The first player,Arabella, wishes to shoot over the second player, Boris, and forthis she needs to be as high above Boris as possible. Arabellajumps at time t=0, and Boris jumps later, at time t_R (his reaction time). Assume that Arabella has notyet 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_{\rm R}, where h_A(t) is the height of the raised hands of Arabella, whileh_B(t) is the height of the raised hands of Boris.
Express the vertical displacement interms of H,g,and t.
Find the vertical displacement D(t) between the raised hands of the two players for the timeperiod after Boris has jumped (t>t_{\rm R}) but before Arabella has landed.
Express your answer in terms oft,t_R, g,and H.
What advice would you give Arabella tominimize the chance of her shot being blocked?