Question

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. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is C

$\sqrt{\frac{3}{2}}$

$H_{max}=\frac{u^{2}si{n}^2\theta }{2g}$
According to problem $\frac{u_1^{2}si{n}^2{45}^{\circ }}{2g}=\frac{u_2^{2}si{n}^2{60}^{\circ }}{2g}$
$\Rightarrow \frac{u_1^2}{u_2^2}=\frac{si{n}^2{60}^{\circ }}{si{n}^2{45}^{\circ }}\Rightarrow \frac{u_1}{u_2}\frac{\frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}}=\sqrt{\frac{3}{2}}$.