Q. Two projectiles thrown from the same point at angles $60{^\circ}$ and $30{^\circ}$ with the horizontal attain the same height. The ratio of their initial velocities is
A) 1
B) 2
C) $\sqrt{3}$
D) $\frac{1}{\sqrt{3}}$
Explanation
(d) $h_{max.} = \frac{v^{2}\sin^{2}\theta}{2g}$
In the given problem, $h_{max.}$ is same in both the cases
$\therefore\ v_{1}^{2}\sin^{2}{60{^\circ}} = v_{2}^{2}\sin^{2}{30{^\circ}}$
or $\frac{v_{1}}{v_{2}} = \frac{\sin{30{^\circ}}}{\sin{60{^\circ}}} = \frac{1}{2} \times \frac{2}{\sqrt{3}} = \frac{1}{\sqrt{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.