Question

Prove that the maximum horizontal range is 4 times of the height attained by the particle.

Answer 1

∵ Range R = \(\frac{u^{2} \sin 2 \theta}{g}\)
and maximum height H = \(\frac{u^{2} \sin ^{2} \theta}{2 g}\)

or R = H \(4 \frac{\cos \theta}{\sin \theta}\) = 4H. cotθ

∵ For maximum range θ = 45°
∴ cot θ = 1
∴ R = 4H