What is the time in fractions of the height H?

Question

An object is shoot straight up to a height of H, when time is equal to T, given H and T find the time of the object at 3/4 the time it takes to get to H, or 3/4T. The result should be in fractions of H.

Answer 1

The time, T, the object takes to fall is the same time it takes to rise to height H.
H = (1/2)gT^2
T^2 = 2H/g
H - h = (1/2)g(T/4)^2
h = H - (1/2)(1/16)gT^2
h = H - (1/2)(1/16)g(2H/g)
h = H - H/16
h = (15/16)H