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
$102=\frac{u^2{\sin }^{2}60^{\circ }}{2g}$
For second stone, maximum height
$h=\frac{u^2{\sin }^{2}30^{\circ }}{2g}$
$\therefore \frac{h}{102}=\frac{{\sin }^{2}30^{\circ }}{{\sin }^{2}60^{\circ }}=\frac{1/4}{3/4}=\frac{1}{3}$ or
$h=\frac{102}{3}=34m$