Finding vertical displacement in terms of a function of two heights.

[thepatient]

So I've been stuck on this problem for hours, I just can't seem to put the pieces together...

Homework Statement

Two basketball players of equal height, (and jumping with same initial velocity, etc.) by jumping they raise their centers of mass the same distance "H". The first player (A) wishes to shoot over the second player (B), for this she needs to be as high above B as possible. A jumps at t=0. B jumps at time t(sub R) his reaction time. Assuming that A doesn't reach maximum height when B jumps.

Find the vertical displacement D(t) =h_A(t) - h_B(t), while h_A(t) is the height of A with raised hands and h_B(t) is the height of B with raised hands.

y_max: H
y₀=0
a= g

Homework Equations

I used equations:
x = x₀ +v₀t+1/2 gt²

and the derivative of that to find the initial velocity.

The Attempt at a Solution

So after thinking for hours and pondering if my approach to the problem was making sense or not, I first tried to get the function of H(t) for player A. I assumed that I would need an initial velocity, so I used the velocity at the max height (which is obviously zero) to calculate it.

v_ya=v_0a+gt
0 = v_0a+gt
v_0a=-gt

So I assumed that was the velocity the instant A jumps.

Then to find the function of the height for A, I used y = y₀ +v₀t+1/2 gt²

Since A begins the jump at y = 0, I assumed the function will be the difference between the max height H and the distance in terms of t. H_a(t) = H -(y₀+v₀(t) +1/2 gt² and ended up with the function of H for a in terms of time is H +1/2 gt². But then after thinking of it it doesn't make sense.

So yes I'm horribly confused, I did great on all the questions in my mastering physics homework, but all the questions that have you figure a height out or a function like this one (which are like three that I have) are so confusing and so hard to put into a formula...And it makes me sad, because I'm usually very good in math, but physics is a whole different type of beast. Thanks in advance guys..

 

[thepatient]

Nevermind... I got it... took me an additional 3 hours... Got an overall score of 92% in my mastering physics assignment... A lot of people in class were having so much trouble in it.