Question

Maximum height of the stone above the ground

Answer 1

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

Answer 2

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