A man at rest observes the rain falling vertically. When he walks at $4 k m / h,$ he has to hold his umbrella at an angle of $53 °$ from the vertical. Find the velocity of raindrop.

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$4 k m / h$

$5 k m / h$

$6 k m / h$

$3 k m / h$

answer is A.

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Detailed Solution

Assigning usual symbols $\vec{v_{m}}, \vec{v_{r}} a n d \vec{v_{r / m}}$ to velocity of man, velocity of rain and velocity of rain relative to man, we can express their relationship by the following equation $\vec{v_{r}} = \vec{v_{m}} + \vec{v_{r / m}}$

The above equation suggests that a standstill man observes velocity $\vec{v_{r}}$ of rain relative to the ground and while he is moving with velocity $\vec{v_{m}}$ , he observes velocity of rain relative to himself $\vec{v_{r / m}}$ . It is a common intuitive fact that umbrella must be held against $\vec{v_{r / m}}$ for optimum protection of rain. According to these facts, direction of velocity vectors are shown in the adjoining figure. Therefore, $v_{r} = v_{m} \tan 37^{\circ} = 3 k m / h$