Question

Rain is falling vertically downwards with a velocity of $4km/h$. A man walks in the rain with a velocity of $3km/h$. 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)

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

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