Two basketball players are essentially equal in all respects. In particular, by jumping they can raise their centers of mass the same vertical distance, H. The first player,Arabella, wishes to shoot over the second player, Boris, and forthis she needs to be as high above Boris as possible. Arabella Jumps at time t=0, and Boris jumps later, at time \(\displaystyle{t}_{{R}}\)(his reaction time). Assume that Arabella has not yet reached her maximum height when Boris jumps.

Part A.) Find the vertical displacement \(\displaystyle{D}{\left({t}\right)}={h}_{{A}}{\left({t}\right)}-{h}_{{B}}{\left({t}\right)}\), as a function of time for the interval \(\displaystyle{0}{<}{t}{<}{t}_{{R}}\), where \(\displaystyle{h}_{{A}}{\left({t}\right)}\) is the height of the raised hands of Arabella, while \(\displaystyle{h}_{{B}}{\left({t}\right)}\) is the height of the raised hands of Boris. (Express thevertical displacement in terms of H,g,and t.)

Part B.) Find the vertical displacement D(t) between the raised hands of the two players for the time period after Boris has jumped (\(\displaystyle{t}{>}{t}_{{R}}\)) but before Arabella has landed. (Express youranswer in terms of t,\(\displaystyle{t}_{{R}}\), g,and H)

Part C.) What advice would you give Arabella To minimize the chance of her shot being blocked?