Question

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

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

Answer 1

The correct option is A $5km/hr$

$\text{Step 1: Velocity of rain and man[Ref. Fig.]}$

The upward direction is positive.

The right direction is positive.

In the figure CA represent the velocity of man and CB represent the velocity of rain

Velocity of rain wrt ground ${\overrightarrow{V}}_r=-3\hat{j}$ $Km/hr$

Velocity of man wrt ground ${\overrightarrow{V}}_m=4\hat{i}$ $Km/hr$

$\text{Step 2: Relative velocity of rain w.r.t man}$

The relative velocity of rain with respect to man:

${\overrightarrow{V}}_{rm}={\overrightarrow{V}}_r-{\overrightarrow{V}}_m$

$=-3\hat{j}-4\hat{i}$

$|{\overrightarrow{V}}_{rm}|=\sqrt{(3^2+4^2)}$

$|{\overrightarrow{V}}_{rm}|=5km/h$

Hence, Option A is correct