Q. Two bodies are thrown up at angles of $45{^\circ}$ and $60{^\circ}$, respectively with the horizontal. If both bodies attain same vertical height , then the ratio of velocities with which these are thrown is
A) $\sqrt{\frac{2}{3}}$
B) $\frac{2}{\sqrt{3}}$
C) $\sqrt{\frac{3}{2}}$
D) $\frac{\sqrt{3}}{2}$
Explanation
(c) $H_{\max} = \frac{u^{2}\sin^{2}\theta}{2g}$
According to problem $\frac{u_{1}^{2}\sin^{2}{45{^\circ}}}{2g} = \frac{u_{2}^{2}\sin^{2}{60{^\circ}}}{2g}$
$\Rightarrow \frac{u_{1}^{2}}{u_{2}^{2}} = \frac{\sin^{2}{60{^\circ}}}{\sin^{2}{30{^\circ}}} \Rightarrow \frac{u_{1}}{u_{2}} = \frac{\sqrt{3}/2}{1/\sqrt{2}} = \sqrt{\frac{3}{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.