Question

A particles is projected with velocity $2\sqrt{gh}$ and at an angle ${60}^o$ to the horizontal so that it just clears two walls of equal height $h$ which are at a distance $2h$ from each other. The time taken by the particle to travel between these two walls is

• A. $2\sqrt{\frac{2h}{g}}$
• B. $\sqrt{\frac{h}{2g}}$
• C. $2\sqrt{\frac{h}{g}}$
• D. $2\sqrt{\frac{h}{2g}}$

Answer 1

The correct option is C $2\sqrt{\frac{h}{g}}$

Velocity of the particle $v=2\sqrt{gh}$
Angle of projection $\theta ={60}^o$
Horizontal component of velocity $v_x=v\cos \theta =2\sqrt{gh}\times 0.5=\sqrt{gh}$
Time taken by particle to travel between two walls $t=\frac{2h}{v_x}$
$⟹t=\frac{2h}{\sqrt{gh}}=2\sqrt{\frac{h}{g}}$