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 these 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

Answer: (D)

$h_{1}=h_{2}$
$\frac{u_{1}^{2} \sin ^{2} 45^{\circ}}{2 g}=\frac{V_{2}^{2} \sin ^{2} 60^{\circ}}{2 g}$
$\frac{u_{1}^{2}}{V_{2}^{2}}=\frac{\frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{3}{2}$
$\frac{V_{1}}{V_{2}}=\sqrt{\frac{3}{2}}$