Question

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

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

Answer 1

The correct option is A $2\sqrt{2}km/h,{45}^o$

The velocity of rain appearing to the man is relative velocity of rain with respect to man.

Thus velocity of rain is = $2\hat{i}+2\hat{j}$
Hence magnitude of velocity is $2\sqrt{2}$ and direction is ${tan}^{-1}\left(\frac{2}{2}\right)={45}^o$