Calculations for a ball tossed vertically upward

[jaewonjung]

Homework Statement

A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance. The answer should be in terms of H.

Relevant Equations

h=vot + 1/2gt^2

I tried to substitute 1/2T in for T, because 1/2 T is when the ball is at H. With that, I found Vo, which was (H-1/8gT^2)/(1/2T).

I plugged in Vo into h=volt+1/2gt^2 and put 1/4 T for t, but I could not get an answer in terms of H

 

[tnich]

I think you might have better luck with this if you say that $t = 0$ when $h_0 = H$.

 

[haruspex]

I tried to substitute 1/2T in for T, because 1/2 T is when the ball is at H. With that, I found Vo, which was (H-1/8gT^2)/(1/2T).

I plugged in Vo into h=volt+1/2gt^2 and put 1/4 T for t, but I could not get an answer in terms of H

Are you taking g to be positive (i.e. 9.81m/s²) or negative?
You have two equations but three unknowns. You have not used the fact that H is the highest height.