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, $45°$
Concept. $\vec v_r = \vec v_{rm} + \vec v_m$.
Step 1. Vectors. East $\hat i$, up $\hat j$: $\vec v_m = 2\hat i$, $\vec v_{rm} = -2\hat j$.
Step 2. Actual rain. $\vec v_r = 2\hat i - 2\hat j$: speed $2\sqrt2$ kmph, equal components, so $45°$ with the vertical.
Answer. $2\sqrt2$ kmph, $45°$ (Option A).
Solution by Sreeraj P, M.Sc Physics