Question

To a stationary man, rain appears to be falling at his back at an angle $30^o$ with the vertical. As he starts moving forward with a speed of $0.5m{s}^{-1},$ he finds that rain falls vertically. The speed of rain with respect to stationary man is

• A. $0.5m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $\frac{\sqrt{3}}{2}m{s}^{-1}$
• D. $\frac{1}{\sqrt{3}}m{s}^{-1}$

Answer 1

Answer: (B)

For stationary person

For running person

Speed of rain with respect to a stationary man $=\nu$
$\overrightarrow{v}=vsin30^o\hat{i}-vcos30^o\hat{j}$
The velocity of rain with respect to man,
${\overrightarrow{v}}_{RM}={\overrightarrow{v}}_R-{\overrightarrow{v}}_M$
$=(vsin{\left(30\right)}^o\hat{i}-vcos{\left(30\right)}^o\hat{j})-(0.5\hat{i})$
Since ${\overrightarrow{V}}_{RM}$ is vertically downward, its $x$ -component will become zero.
$\therefore vsin30^o-0.5=0$
$\Rightarrow v=\frac{0.5}{sin30^o}=1m{s}^{-1}$