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Q.

When a man is standing, rain drops appears to him falling at 60^o from the horizontal from his front side. When he is travelling at 5 kmph on a horizontal road they appear to him falling at 30⁰ from the horizontal from his front side. The actual speed of the rain is (in kmph)

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a

5 $\sqrt{3}$

b

3

c

4

d

5

answer is C.

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Detailed Solution

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$\tan 60^{o} = \frac{V_{R} \sin 60}{V_{R} \cos 60} . . . . (1)$

$\tan 30^{o} = \frac{V_{R} \sin 60^{o}}{V_{R} \cos 60^{o} + 5} . . . . (2)$

From (1) and (2).

$\frac{V_{R} \cos 60^{o} + 5}{V_{R} \cos 60^{o}} = 3 \Rightarrow V_{R} = 5 kmph$

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When a man is standing, rain drops appears to him falling at 60o from the horizontal from his front side. When he is travelling at 5 kmph on a horizontal road they appear to him falling at 300 from the horizontal from his front side. The actual speed of the rain is (in kmph)