Question

Two stones having different masses m₁ and m₂ are projected at an angle $α$ and (90° $- α$ ) with same speed from same point. The ratio of their maximum heights is

Moderate

Solution

Maximum height, $H = \frac{u^{2} \sin^{2} α}{2 g} \Rightarrow H \propto \sin^{2} α$
$∴ \frac{H_{1}}{H_{2}} = \frac{\sin^{2} α}{\sin^{2} (90 ° - α)} = \tan^{2} α$

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