Question

Two objects are thrown up at angles of ${45}^{\circ }$ and ${60}^{\circ }$ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which they are projected is

• A. $\sqrt{\frac{5}{3}}$
• B. $\sqrt{\frac{3}{5}}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\sqrt{\frac{3}{2}}$

Answer 1

The correct option is D $\sqrt{\frac{3}{2}}$

Maximum height attained by the projectile is given by
$H=\frac{u^2{\sin }^2\theta }{2g}$
According to question.
$H_1(\text{at}\theta ={45}^{\circ })=H_2(\text{at}\theta ={60}^{\circ })\Rightarrow \frac{u_1^2{\sin }^2{45}^{\circ }}{2g}=\frac{u_2^2{\sin }^2{60}^{\circ }}{2g}\Rightarrow \frac{u_1^2}{u_2^2}=\frac{\frac{3}{4}}{\frac{1}{2}}=\frac{3}{2}\Rightarrow \frac{u_1}{u_2}=\sqrt{\frac{3}{2}}$