Question

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 vertically downward direction. The relative velocity of the rain with respect to man is -

• A. $\sqrt{13}\text{km/hr}$
• B. $\sqrt{7}\text{km/hr}$
• C. $\sqrt{109}\text{km/hr}$
• D. $13\text{km/hr}$

Answer 1

The correct option is C $\sqrt{109}\text{km/hr}$

Velocity of man can be written as
$\overrightarrow{V_M}=3\hat{i}$
Velocity of rain can be written as
$\overrightarrow{V_R}=-10\hat{j}$
Relative velocity
${\overrightarrow{V}}_{RM}=\overrightarrow{V_R}-\overrightarrow{V_M}=-10\hat{j}-3\hat{i}\Rightarrow |{\overrightarrow{V}}_{RM}|=\sqrt{109}\text{km/hr}$