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  4. A man running at a speed of 5 km/h , find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of 60° with the horizontal. The velocity of rain with respect to running man is

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Q. A man running at a speed of $ 5\,km/h $ , find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of $ 60^{\circ} $ with the horizontal. The velocity of rain with respect to running man is

EAMCETEAMCET 2015

Solution:

Consider the situational diagram as shown below.
image
In $\triangle O A P$,
$ \tan 30^{\circ}= \frac{v_{m}}{v_{m}} $
$=\frac{\text { Velocity of man }}{\text { Velocity of rain with respect to man }} $
$ \Rightarrow v_{I m} =\frac{5}{1 / \sqrt{3}} $
$=5 \sqrt{3}\, km / h $