Question

A stationary man observes that the rain strikes him at an angle of ${60}^{\circ }$ to the horizontal. When he begins to move with the velocity of $25m/s$ then the drops appear to strike him at an angle ${30}^{\circ }$ from horizontal. The velocity of the rain drops is :

• A. $25m/s$
• B. $50m/s$
• C. $12.5m/s$
• D. $25\sqrt{2}$

Answer 1

The correct option is A $25m/s$

let velocity of rain is $v$ then

Horizontal component = $vcos60=\frac{v}{2}$

Vertical component =$vsin60=\frac{\sqrt{3}v}{2}$

When he begins to move with a velocity of $25m/s$ then the drops appear

with horizontal velocity = $\frac{v}{2}+25$

then $tan30=\frac{\frac{\sqrt{3}v}{2}}{\frac{v}{2}+25}$

so,

$v+50=3v$

Then,

$v=25m/s$

The velocity of the rain drop is $25m/s$.

Hence, Option A is correct.