A man is walking on a road with a velocity $3\text{km/hr}$. Suddenly rain starts falling. The velocity of rain is $10\text{km/hr}$ in a vertically downward direction. The relative velocity of the rain with respect to man is -

The correct option is C $\sqrt{109}\text{km/hr}$
Let a man walking along the positive $x-$ direction and rain falling along the negative $y-$direction.

The velocity of man can be written as
${\overrightarrow{V}}_M=3\hat{i}$
The velocity of rain can be written as
${\overrightarrow{V}}_R=-10\hat{j}$

Relative velocity
${\overrightarrow{V}}_{RM}={\overrightarrow{V}}_R-{\overrightarrow{V}}_M=-10\hat{j}-3\hat{i}\Rightarrow |{\overrightarrow{V}}_{RM}|=\sqrt{109}\text{km/hr}$