Question

A shower of rain appears to fall vertically downwards with a velocity $12km/h$ on a person walking westwards with a velocity of $5km/h$. The actual velocity and direction of the rain is

• A. $8.5km/h$ clockwise to vertical.
• B. $13km/h$, anticlockwise to vertical.
• C. $13km/h$, clockwise to vertical.
• D. $8.5km/h$, vertically downwards.

Answer 1

The correct option is C $13km/h$, clockwise to vertical.

Given,
A shower of rain APPEARS to fall vertically downwards, it means it is not the actual velocity of the rain.
$\therefore \overrightarrow{OA}=-12\hat{j}$
Also,
$\overrightarrow{AB}=-5\hat{i}$
Thus,
$\overrightarrow{OB}=-12\hat{j}-5\hat{i}$
$\therefore |\overrightarrow{OB}|=\sqrt{{12}^2+5^2}=13kmph$