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Relative Motion: Rain Example

Rain falling ...

Question

Rain falling vertically downwards with a velocity of $3 k m h^{- 1}$ . A person moves on a straight road with a velocity of $4 k m h^{- 1}$ . Then, the apparent speed of the rain with respect to the person is

1 k m h^{- 1}

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5 k m h^{- 1}

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4 k m h^{- 1}

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3 k m h^{- 1}

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Solution

The correct option is B $5 k m h^{- 1}$
$r =$ rain $, g =$ ground $& m =$ man
$v_{r g} = - 3^j$ , $v_{m g} = - 4^i$
We have, $_{r m} =_{r g} -_{m g} = - 4^j - 4^i$
$v_{r m} = \sqrt{{v_{r g}}^{2} + {v_{m g}}^{2}} = \sqrt{3^{2} + 4^{2}} = 5 k m / h r$

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