Question

Two bodies are thrown up at angles of $40^{\circ}$ and $60^{\circ}$ respectively, with the horizontal. If both bodies attain same vertical height, then ratio of velocities with which these are thrown is

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

Answer 1

Answer: (C)

$\sqrt { 3 / 2}$

Answer 2

$\frac{u_{1}^{2} \sin ^{2} \theta_{1}}{2 g}=\frac{u_{2}^{2} \sin ^{2} \theta_{2}}{2 g}$
or $\frac{u_{1}}{u_{2}}=\frac{\sin \theta_{2}}{\sin \theta_{1}}$
or $\frac{u_{1}}{u_{2}}=\frac{\sin 60^{\circ}}{\sin 45^{\circ}}$
or $\frac{u_{1}}{u_{2}}=\frac{\sqrt{3} / 2}{1 / \sqrt{2}}$
or $\frac{u_{1}}{u_{2}}=\sqrt{\frac{3}{2}}$