Question

A man is walking due east at the speed of $3\text{km/h}$. Rain appears to fall down vertically at the rate of $3\text{km/h}$. The magnitude of actual velocity of the rain is

• A. $3\text{km/h}$
• B. $3\sqrt{2}\text{km/h}$
• C. $6\text{km/h}$
• D. $9\text{km/h}$

Answer 1

The correct option is B $3\sqrt{2}\text{km/h}$

Velocity of man, $v_m=3\text{km/h}$ due East
Velocity of rain w.r.t man, $v_{rm}=3\text{km/h}$ vertically downwards.
Actual velocity of rain $=v_r$


From the figure, we have $v_r^2=v_{rm}^2+v_m^2$
$v_r^2=3^2+3^2$
Hence, we get, $v_r=3\sqrt{2}\text{km/h}$
The correct option is (b).