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Relative Velocity in 2D

A man moving ...

Question

A man moving at 4 km per hour towards East finds the raindrops falling vertically at 4 km per hour. What is the actual speed and direction of rain?

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Solution

Actual speed of rain = $|_{r} | = \sqrt{4^{2} + 4^{2}} = 4 \sqrt{2} k m / h$
$tan θ = \frac{V_{r m}}{V_{m}} = \frac{4}{4} = 1$
$\Rightarrow θ = 45^{\circ}$

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