Question

A man is walking due west at the rate of $5km/h$.The rain appears to him to come down vertically at the rate of $5km/h$. The actual velocity and direction of rainfall with the vertical respectively are

• A. $5\sqrt{2}km/h,{45}^o$
• B. $\frac{1}{\sqrt{2}}km/h,{30}^o$
• C. $5km/h,0^o$
• D. $1km/h,{90}^o$

Answer 1

The correct option is A $5\sqrt{2}km/h,{45}^o$

$V_{Rain,Person}=V_{Rain}-V_{Person}=-5\hat{j}$ (vertically down)
Thus, $V_{Rain}-(-5\hat{i})=-5\hat{j}$ (west means $-5\hat{i}$)
or, $V_{Rain}=-5\hat{i}-5\hat{j}$
Thus, magnitude = $5\sqrt{2}$ km/hr, direction is in 3rd quadrant, i.e. clockwise to vertical at an angle of $ta{n}^{-1}\left(\frac{5}{5}\right)={45}^o$ to vertical