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 .5 m s - 1 , he finds that rain falls vertically. The spee

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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 .5 m s - 1 , he finds that rain falls vertically. The speed of rain with respect to stationary man is

TestHub · Accepted Answer

For stationary person

For running person

Speed of rain with respect to a stationary man $= ν$
$\vec{v} = v \sin 30^{o} \hat{i} - v \cos 30^{o} \hat{j}$
The velocity of rain with respect to man,
${\vec{v}}_{R M} = {\vec{v}}_{R} - {\vec{v}}_{M}$
$= (v \sin 30^{o} \hat{i} - v \cos 30^{o} \hat{j}) - (0.5 \hat{i})$
Since ${\vec{V}}_{R M}$ is vertically downward, its $x$ -component will become zero.
$∴ v \sin 30^{o} - 0.5 = 0$
$\Rightarrow v = \frac{0.5}{\sin 30^{o}} = 1 m s^{- 1}$

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