Q.32(b):- Shows that the projection angle θ⁰ for a projectile launched from the origin is given by θ₀ = tan^-1(4h_m / R)
where the symbols have their usual meaning.

Answer:- 

Maximum vertical height, h_m = u₀² Sin²θ / 2g   …(i)
Horizontal range, R = u₀² Sin²2θ / g   … (ii)
h_m / R = Sin²θ / 2Sin²2θ
= Sin θ X Sin θ / 2 X 2SinθCosθ
= Sin θ / 4 Cos θ = tan θ / 4
tan θ = (4h_m / R)
θ = tan^-1 (4h_m / R)