Question

Two balls are projected from the same point in directions inclined at ${60}^{\circ }$ and ${30}^{\circ }$ to the horizontal. If they attain the maximum height at the same time, what is the ratio of their velocities of projection?

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{1}{3}$
• C. $\sqrt{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{\sqrt{3}}$

Time of flight, $T=\frac{2u\sin \theta }{g}$
Since their time of ascent are same
$\frac{u_1\sin {60}^{\circ }}{g}=\frac{u_2\sin {30}^{\circ }}{g}$
$\frac{u_1}{u_2}=\frac{1}{\sqrt{3}}$