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Q.

A man is walking due east at the rate of 4kmph and the rain is falling at an angle of $30°$ east of vertical with a velocity of 6kmph. The velocity of the rain relative to the man will be

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a

8.718 kmph

b

10 kmph

c

7.718 kmph

d

5 kmph

answer is A.

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Detailed Solution

Question Image

${\vec{v}}_{m r} = {\vec{v}}_{r} + (- {\vec{v}}_{m})$

$v_{rm} = \sqrt{v_{p}^{2} + v_{m}^{2} + 2 v_{r} (- v_{m}) \cos 150 °}$

$= \sqrt{36 + 16 + 2 (4)} (\frac{1}{2}) = \sqrt{52 + 24}$

$= \sqrt{76} = 8.718 kmph$

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