question_answer

Rain is falling vertically downwards with a velocity of 4 km/h. A man walks in the rain with a velocity of 3 km/h. The raindrops will fall on the man with a velocity of

A)  1 km/h                                

B)  3 km/h

C)  4 km/h                                

D)  5 km/h

Correct Answer: D

Solution :

                 Relative velocity of man w.r.t. rain, \[{{\overrightarrow{v}}_{rm}}={{\overrightarrow{v}}_{{{r}^{-}}}}-{{\overrightarrow{v}}_{m}}\] \[=4\hat{j}-3\hat{i}\] \[=-3\hat{i}+4\hat{j}\] or \[=5km/h\,|{{\overrightarrow{v}}_{rm}}|=\sqrt{{{(-3)}^{2}}+{{(4)}^{2}}}\]                 \[=\sqrt{9+16}\]                 \[=\sqrt{25}\]