Q.32(b):- Shows that the projection angle θ0 for a projectile launched from the origin is given by θ0 = tan-1(4hm / R)
where the symbols have their usual meaning.
Answer:-
Maximum vertical height, hm = u02 Sin2θ / 2g …(i)
Horizontal range, R = u02 Sin22θ / g … (ii)
hm / R = Sin2θ / 2Sin22θ
= Sin θ X Sin θ / 2 X 2SinθCosθ
= Sin θ / 4 Cos θ = tan θ / 4
tan θ = (4hm / R)
θ = tan-1 (4hm / R)