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 $102m$. Then the maximum height reached by the other in metre is

• A. 336
• B. 224
• C. 56
• D. 34

Answer 1

Answer: (D)

Key Idea Horizontal ranges are same for complementary angles of projection ie, for $\theta$ and $\left(90^{\circ }-\theta \right)$
We know that if two stones have same horizontal range, then this implies that both are projected at $\theta$ and $90^{\circ }-\theta$
Here, $\theta =\frac{\pi }{3}=60^{\circ }$
$\therefore 90^{\circ }-\theta =90^{\circ }-60^{\circ }=30^{\circ }$
For first stone, Max. height $=102=\frac{u^2{\sin }^{2}60^{\circ }}{2g}$
For second stone, Max. height, $h=\frac{u^2{\sin }^{2}30^{\circ }}{2g}$
$\therefore \frac{h}{102}=\frac{{\sin }^{2}30^{\circ }}{{\sin }^{2}60^{\circ }}=\frac{(1/2{)}^2}{(\sqrt{3}/2{)}^2}$
or $h=102\times \frac{1/4}{3/4}=34m$