get vetical component of velocity up at ground, call it Vi. If shot at angle A up from horizontal then Vi = V sin A
during flight acceleration = -g or 9.8 m/s^2 down or 32 ft/s^2 down
speed up = v = Vi - g t
= Vi -9.8 t or = Vi -32 t
at top, v = 0
so
t = Vi/9.8 or t = Vi/32
then h = Vi t -(9.8/2)t^2
or h = Vi t - 16 t^2
Maximum height of the stone above the ground
2 answers
alternatively you can use conservation of energy
kinetic energy at bottom = potenial energy at top
(1/2)mVi^2 = m g h
so
Vi^2 = (2 g h)
h = Vi^2/2g
kinetic energy at bottom = potenial energy at top
(1/2)mVi^2 = m g h
so
Vi^2 = (2 g h)
h = Vi^2/2g