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

NTA AbhyasNTA Abhyas 2020Motion in a Plane

Solution:

$V_{r}= \, \text{velocity of rain} \\ \, \\ \text{V}_{\text{rm}}=\text{ velocity of rain with respect to man} \\ \\ \text{V}_{\text{m}}=\text{ velocity of man}$
Solution
$tan 30^{o}=\frac{V_{m}}{V_{r m}}$
$V_{r m}=\frac{5}{\frac{1}{\sqrt{3}}}=5\sqrt{3} \, km/h$