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A man moves on a straight road with a velocity of 3 km/h. Rain is falling vertically with a speed of $3 \sqrt{3} k m / h$ . At what angle with vertical should the man hold his umbrella to protect himself from rain water?

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$30^{o}$

$45^{o}$

$60^{o}$

$37^{o}$

answer is B.

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Detailed Solution

$ω_{c}$ know, $\vec{V_{R}} = \vec{V_{m}} + {\vec{V_{}}}_{R / m}$

The velocity triangle is as shown in figure.

$∴ \tan θ = \frac{V_{m}}{V_{R}} = \frac{3}{3 \sqrt{3}} \Rightarrow θ = 30^{o}$

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