Q 11-03-010NEETJEE MainEAMCET 2008 (Medical)Medium
A man is walking due east at the rate of $2$ kmph. The rain appears to him to come down vertically at the rate of $2$ kmph. The actual velocity and direction of rainfall with the vertical respectively are
Answer: (A) $2\sqrt{2}$ kmph, $45°$
Take east as $\hat{i}$ and vertically up as $\hat{j}$. Man: $\vec{v}_m = 2\hat{i}$. Rain relative to the man: $\vec{v}_{rm} = -2\hat{j}$.
$$\vec{v}_r = \vec{v}_{rm} + \vec{v}_m = 2\hat{i} - 2\hat{j}$$
Speed $= 2\sqrt{2}$ kmph. The horizontal and vertical components are equal, so the rain falls at $45°$ to the vertical (towards the east).
Solution by Sreeraj P, M.Sc Physics