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Throwing and Catching at Same Height

A man moving ...

Question

A man moving with $5 m s^{- 1}$ observes rain falling vertically at the rate of $10 m s^{- 1}$ . Find the speed and direction of the rain with respect to ground.

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Solution

${\to v}_{r, m} = - 10^j m s^{- 1}, {\to v}_{m} = 5^i m s^{- 1}$
${\to v}_{r, m} = {\to v}_{r} - {\to v}_{m}$
${\to v}_{r} = {\to v}_{r, m} + {\to v}_{m} = (- 10^j) + (5^i) m s^{- 1}$
$\Rightarrow | {\to v}_{r} | = 5 \sqrt{5} m s^{- 1}$
Inclination of the rain with vertical, $t a n θ = \frac{1}{2}$
$\Rightarrow θ = t a n^{- 1} \frac{1}{2}$

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