Question

Two projectiles having different masses $m_{1}$ and $m_{2}$ are projected at an angle $\alpha$ and $\left(90^{\circ}-\alpha\right)$ with the same speed from some point. The ratio of their maximum heights is

• A. $\cot \alpha: \sin \alpha$
• B. $1: 1$
• C. $\tan ^{2} \alpha: 1$
• D. $1: \tan \alpha$

Answer 1

Answer: (C)

Maximum height, $H=\frac{u^{2} \sin ^{2} \alpha}{2 g}$
For same speed of projection,
$H \propto \sin ^{2} \alpha$
$\therefore \frac{H_{1}}{H_{2}} =\frac{\sin ^{2} \alpha}{\sin ^{2}\left(90^{\circ}-\alpha\right)}$
$=\frac{\sin ^{2} \alpha}{\cos ^{2} \alpha}=\tan ^{2} \alpha$