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Relative Motion: Rain Example

A man is walk...

Question

A man is walking due east at the speed of $3 km/h$ . Rain appears to fall down vertically at the rate of $3 km/h$ . The magnitude of actual velocity of the rain is

A

3 km/h

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B

3 \sqrt{2} km/h

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C

6 km/h

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D

9 km/h

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Solution

The correct option is B $3 \sqrt{2} km/h$
Velocity of man, $v_{m} = 3 km/h$ due East
Velocity of rain w.r.t man, $v_{r m} = 3 km/h$ vertically downwards.
Actual velocity of rain $= v_{r}$

From the figure, we have $v_{r}^{2} = v_{r m}^{2} + v_{m}^{2}$
$v_{r}^{2} = 3^{2} + 3^{2}$
Hence, we get, $v_{r} = 3 \sqrt{2} km/h$
The correct option is (b).

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