Rain is falling vertically downwards with a velocity of 4 km h^–1. A man walks in the rain with a velocity of 3 km h^–1. The raindrops will fall on the man with a velocity of:

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$1 {kmh}^{- 1}$

$3 {kmh}^{- 1}$

$4 {kmh}^{- 1}$

$5 {kmh}^{- 1}$

answer is D.

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Detailed Solution

Velocity relative to the man is ${\vec{V}}_{rm}$
Now ${\vec{V}}_{rm} = {\vec{V}}_{r} - {\vec{V}}_{m}$
$∴ V_{rm} = \sqrt{V_{r}^{2} + V_{m}^{2}} = \sqrt{4^{2} + 3^{2}} km / h = 5 km / h$ .

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