Question

Rain is falling vertically downwards with a velocity of $3\text{kmph}$. A man walks in the rain with a velocity of $4\text{kmph}$. The rain drops will fall on the man with a velocity of:

• A. $1\text{kmph}$
• B. $3\text{kmph}$
• C. $4\text{kmph}$
• D. $5\text{kmph}$

Answer 1

The correct option is D $5\text{kmph}$



Velocity of rain w.r.t. ground,
${\overrightarrow{V}}_{rg}=-3\hat{j}\text{km/h}$
Velocity of man w.r.t. ground,
${\overrightarrow{V}}_{mg}=4\hat{j}\text{km/h}$
Velocity of rain w.r.t. man,
${\overrightarrow{V}}_{rm}={\overrightarrow{V}}_{rg}-{\overrightarrow{V}}_{mg}{\overrightarrow{V}}_{rm}=(-3\hat{j}-4\hat{i})\text{km/h}\left|{\overrightarrow{V}}_{rm}\right|=\sqrt{(-3{)}^2+(-4{)}^2}=\sqrt{25}=5\text{km/h}$