For a man walking towards east with a velocity of 5 km/hr, rain appears to fall vertically down. When the man begins to walk towards west with a velocity of 3 km/hr the rain appears to fall at an angle of $60^{o}$ to the vertical. The magnitude of velocity of the rain when the man stops walking is

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$\sqrt{\frac{139}{3}}$

$\sqrt{\frac{139}{4}}$

$\sqrt{\frac{139}{6}}$

$\sqrt{\frac{139}{5}}$

answer is A.

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Detailed Solution

velocity of rain= $x \hat{i} + y \hat{j}$

Velocity of man= 5 $\hat{i}$

x-5=0

x= 5

Now, 2nd case, x+3=5+3=8

$\frac{8}{y} = \tan 60; y = \frac{8}{\sqrt{3}}$

Magnitude of velocity of rain= $\sqrt{5^{2} + \frac{64}{3}} = \sqrt{\frac{139}{3}}$

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