Question

Two particles are projected simultaneously with same speed $V_{0}$ in same vertical plane at angles $30^{o}$ and $60^{o}$ with the horizontal. The time at which their velocities becomes parallel is

• A. $\frac{V_{0}}{2 g}$
• B. $V_{0}\left(\frac{\sqrt{3} + 1}{2 g}\right)$
• C. $\frac{\sqrt{3} \, V_{0}}{2 g}$
• D. $\frac{V_{0} \left(\sqrt{3} - 1\right)}{g}$

Answer 1

Answer: (B)

$\overset{ \rightarrow }{V_{1}}=V_{0}cos \left(30\right)^{o}\hat{i}+\left(V_{0} sin ⁡ \left(30\right)^{o} - g t\right) \, \hat{j}$
$\overset{ \rightarrow }{V_{2}}=V_{0}cos \left(60\right)^{o}\hat{i}+\left(V_{0} sin ⁡ \left(60\right)^{o} - g t\right) \, \hat{j}$
$\because \, \, \, \overset{ \rightarrow }{V_{1}}\left|\right.\left|\right. \, \overset{ \rightarrow }{V_{2}} \, $
$\Rightarrow \, \, \, \frac{V_{0} cos 30^{o}}{V_{0} cos ⁡ 60^{o}}=\frac{V_{0} sin ⁡ 30^{o} - g t}{V_{0} sin ⁡ 60^{o} - g t}$
$\Rightarrow \, t=\frac{V_{0} \left(\sqrt{3} + 1\right)}{2 g}$