Question

Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $\pi / 3$ and the maximum height reached by it is 102 metres. Then the maximum height reached by the other in metres is

• A. 336
• B. 224
• C. 56
• D. 34

Answer 1

Answer: (D)

Horizontal range will be same if angles of projection are
$\theta$ and $\left(90^{\circ}-\theta\right)$.
When $\theta=\frac{\pi}{3}=60^{\circ},$ then $\left(90^{\circ}-\theta\right)=90^{\circ}-60^{\circ}=30^{\circ}$
For first stone, maximum height
$102=\frac{u^{2} \sin ^{2} 60^{\circ}}{2 g}$
For second stone, maximum height
$h=\frac{u^{2} \sin ^{2} 30^{\circ}}{2 g}$
$\therefore \frac{h}{102}=\frac{\sin ^{2} 30^{\circ}}{\sin ^{2} 60^{\circ}}=\frac{1 / 4}{3 / 4}=\frac{1}{3}$ or
$ h=\frac{102}{3}=34 m$