Question

A person observes that rain strikes him normally when he is moving with $2$ kmph. When he reverses his direction and moves with the same speed, the rain will strike him at an angle ${45}^o$ with the vertical. The true velocity of rain fall is:

• A. $2$ kmph
• B. $\sqrt{2}$kmph
• C. $5\sqrt{2}$kmph
• D. $2\sqrt{5}$kmph

Answer 1

Answer: (D)

$2\sqrt{5}$kmph

Let the velocity of rain will be

See image 3

In case $1$

$V_{Rain}-V_{man}$=See image 4

$\Rightarrow V_{Rx}=V_{man}=2km/hr$

In case $2$

$V_{Rain}=V_{man}$= See image 5

$\left(V_{rain/man}\right)\cos 45°=V_{max}+V_{Rx}\left(V_{rain/man}\right)\cos 45°=V_{Ry}$

$\Rightarrow V_{Ry}=V_{man}+V_{Rx}=2+24km/hr$

Actual velocity of rain $=\sqrt{V_{Rx}^2+V_{Ry}^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}km/hr$