For fixed projection speed u, the quantity RᵖHᑫ is to be maximized, where p, q>0. The optimum projection angle satisfies:
Options

Question

For fixed projection speed u, the quantity RᵖHᑫ is to be maximized, where p,q>0. The optimum projection angle satisfies:

G1 Physics · Accepted Answer

For fixed u, R ∝ sinθ cosθ, H ∝ sin²θ. Therefore RᵖHᑫ ∝ sinᵖθ cosᵖθ × sin²ᑫθ = sin⁽ᵖ⁺²ᑫ⁾θ cosᵖθ. For maximum value, (p+2q)cotθ − p tanθ = 0. Hence p tan²θ = p+2q, so tan²θ = (p+2q)/p.