urse Home Chapter 2 HW tem 15 15 of 25> Constants Part A Two basketball players

Question

urse Home Chapter 2 HW tem 15 15 of 25> Constants Part A 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 t0, and Boris jumps later, at time tR (his reaction time). Assume that Arabella has not yet reached her maximum height when Boris jumps Find the vertical displacement D(t) ha(t) h(t), as a function of time for the interval O

Explanation / Answer

A)we know that

v0 = sqrt (2 g H)

from eqn of motion

S = ut + 1/2 at^2

xa = v0t - 1/2 g t^2

xa = sqrt(2gH)t - 1/2 gt^2

bx = (t - tr)sqrt (2gH) - 1/2 g (t - tr)^2

xa - xb = tr sqrt (2gH) - 1/2 g t^2 - (t - tr)^2

dX = tr sqrt(2 g H) - 1/2 g (tr - 2t)

for t < tr

dh = sqrt(2gH)t - 1/2 g t^2

b)for t > tr

dh = sqrt (2 g H)tr + 1/2 g (tr - 2t)

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