Question

Two balls are projected from the same point in directions inclined at ${60}^{0}and{30}^0$ to the horizontal. If they attain the same height, the ratio of their velocity of projection would be (g = 9.8 $m{s}^{-2})$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let $V_{1}and{V}_2$ be the velocities of projection corresponding to angles of projection ${\theta }_1={60}^0,and{\theta }_2={30}^0$.
The maximum height is given by H = $\frac{v_0^{2}si{n}^2\theta }{2g}$
$\therefore H_1=H_2$
$\Rightarrow \frac{v_1^{2}si{n}^2{\theta }_1}{2g}$= $\frac{v_2^{2}si{n}^2{\theta }_2}{2g}$
$\therefore \frac{V_1}{V_2}=\frac{sin{\theta }_2}{sin{\theta }_1}=\frac{1}{\sqrt{3}}$