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Displacement in 2D Motion

A man walks i...

Question

A man walks in rain with a velocity of $5 k m h^{- 1}$ . The raindrops strike at him at an angle of $45^{\circ}$ with the horizontal. The velocity of the rain, if it is falling vertically downward would be

A

5 k m h^{- 1}

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B

4 k m h^{- 1}

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C

3 k m h^{- 1}

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D

1 k m h^{- 1}

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Solution

The correct option is A $5 k m h^{- 1}$
Given that the velocity with which the man walks is $5 k m h^{- 1}$
And angle with horizontal $θ = 45^{\circ}$
From basic trigonometry we know that:
$t a n θ = \frac{v e r t i c a l c o m p o n e n t}{h o r i z o n t a l c o m p o n e n t}$
$t a n 45^{\circ} = 1$
i.e. vertical component = horizontal component $= 5 k m h^{- 1}$
Hence the rain is falling with $5 k m h^{- 1}$

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