A projectile motion is characterized by a motion whose path is alike to that of an arc. It already has its derived equations. For the maximum height H and the maximum range R, the equations are:
H = v₀²sin²θ/2g ; R = v₀²sin(2θ)/g
As you can observe, they are almost alike. Since they both contain v₀²/g, let's isolate this term for both equations:
v₀²/g = 2H/sin²θ
v₀²/g = R/sin (2θ)
Equating both equations:
2H/sin²θ = R/sin (2θ)
H = Rsin²θ/2sin(2θ)
This is the equation that relates H to R.
