Question

Rain is falling vertically downwards with a velocity of $4km/h$. A man walks in the rain with a velocity of $3km/h$. The raindrops will fall on the man with a velocity of magnitude

• A. $1km/h$
• B. $3km/h$
• C. $4km/h$
• D. $5km/h$

Answer 1

The correct option is D $5km/h$

Velocity of rain , $\overrightarrow{v_r}=-4\hat{j}$
Velocity of man, $\overrightarrow{v_m}=3\hat{i}$
Let ${\overrightarrow{v}}_{rm}$ be the velocity of rain w.r.t man
We know that ${\overrightarrow{v}}_{rm}={\overrightarrow{v}}_r-{\overrightarrow{v}}_m$
$=-4\hat{j}-3\hat{i}$ $\therefore |{\overrightarrow{v}}_{rm}|=\sqrt{(-4{)}^2+(-3{)}^2}=\sqrt{25}=5km/h$