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

(a) 2√2 kmph , 45°

(b) 1/√2 kmph , 30°

(c) 2 kmph , 0°

(d) 1 kmph , 90°

Ans:(a)

Sol: $ \displaystyle \vec{v_m} = 2\hat{i}$

$\displaystyle \vec{v_{rm}} = -2\hat{j}$

$ \displaystyle \vec{v_r} = \vec{v_{rm}} + \vec{v_m}$

$ \displaystyle \vec{v_r} = -2\hat{j} + 2\hat{i} $