Question

A man is walking due east at the rate of 2 km/h. The rain appears to him to come down vertically at the rate of 2 km/h. The actual velocity and direction of rainfall with the vertical respectively are

• A. $ 2\sqrt{2}\,km/h,{{45}^{0}} $
• B. $ \frac{1}{\sqrt{2}}\,km/h,{{30}^{0}} $
• C. $ 2\,km/h,{{0}^{0}} $
• D. $ 1\,km/h,{{90}^{0}} $

Answer 1

The Correct Option is A

Velocity of man, $ {{v}_{m}}=2\,km/h $ Velocity of rain, $ {{v}_{r}}=2\,km/h $ Then actual velocity $ {{v}_{rm}}=\sqrt{v_{m}^{2}+v_{r}^{2}} $ $ =\sqrt{{{(2)}^{2}}+{{(2)}^{2}}} $ $ =\sqrt{4+4}=2\sqrt{2}\,km/h $ The direction of rainfall with the vertical $ \sin \theta =\frac{{{v}_{r}}}{{{v}_{rm}}} $ $ =\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}} $ $ \theta ={{\sin }^{-1}}\left( \frac{1}{\sqrt{2}} \right) $ $ \theta ={{45}^{o}} $