Question

A man is walking on a road with a velocity $3km/h$. Suddenly rain starts falling. Velocity of rain is $10km/h$ in vertically downward direction. The relative velocity of the rain with respect to man is

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

Answer 1

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

$\Rightarrow {\overrightarrow{v}}_m=3\hat{i}km/hr$.
${\overrightarrow{v}}_r=10\hat{j}km/hr$
${\overrightarrow{v}}_{rm}={\overrightarrow{v}}_r-{\overrightarrow{v}}_m=(10\hat{j}-3\hat{i})km/h$

$v_{rm}=\sqrt{(3{)}^2+(10{)}^2}=\sqrt{109}km/h$