Question

A man standing on a road has to hold his umbrella at ${60}^{\circ }$ with the horizontal to keep the rain away. He throws the umbrella and starts running at $20km{h}^{-1}$ . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is

• A. $20km{h}^{-1}$
• B. $30km{h}^{-1}$
• C. $40km{h}^{-1}$
• D. $15km{h}^{-1}$

Answer 1

The correct option is C $40km{h}^{-1}$

When the man is at rest with respect to the ground, the rain comes to him at an angle ${30}^{\circ }$ with the vertical. This is the direction of the velocity of raindrops with respect to the ground.

Here, $v_{rg}=$ velocity of the rain w.r.t. the ground and $v_{mg}$ is the velocity of man w.r.t. the ground.



From figure,
$\sin {30}^{\circ }=\frac{v_{mg}}{v_{rg}}$
or $v_{rg}=\frac{v_{mg}}{\sin {30}^{\circ }}$
$=\frac{20}{1/2}=40km{h}^{-1}$