Question

Rain is falling vertically downwards with a velocity of $4\, km / h$. A man walks in the rain with a velocity of $3 \,km / h$. The raindrops will fall on the man with a velocity of

• A. 1 km/h
• B. 3 km/h
• C. 4 km/h
• D. 5 km/h

Answer 1

Answer: (D)

5 km/h

Answer 2

Relative velocity of man w.r.t. rain,

$\vec{v}_{r m}=\vec{v}_{r}-\vec{v}_{m}$
$=4 \hat{j}-3 \hat{i}$
$=-3 \hat{i}+4 \hat{j}$
or $=5\, km/h|$
$\left|\vec{v}_{r m}\right|=\sqrt{(-3)^{2}+(4)^{2}}$
$=\sqrt{9+16}$
$=\sqrt{25}=5$