Question

how do i find maximum height (meters) and initial velocity (m/s) if i have the time (seconds), horizontal range, and horizontal velocity

Answer 1

time up equals time down ... Tu = Td

half of the flight time (Tu) is spent climbing to the max
... h = 1/2 g (Tu)^2

the vertical velocity equals ... g Tu

initial velocity is the vector sum of the vertical and horizontal
... V^2 = (Vh)^2 + (Vv)^2