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. $2km/h,0^0$
• D. $1km/h,{90}^0$

Answer 1

Answer: (A)

Velocity of man, $v_m=2km/h$ Velocity of rain, $v_r=2km/h$ 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
$\sin \theta =\frac{v_r}{v_{rm}}$ $=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$ $\theta ={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$ $\theta ={45}^o$