Question

A shower of rain appears to fall vertically downwards with a velocity $4km/h$ on a person walking westwards with a velocity of $3km/h$. The actual velocity and direction of the rain is

• A. $1km/h$ clockwise to vertical
• B. $5km/h$, anticlockwise to vertical
• C. $5km/h$, clockwise to vertical
• D. $1km/h$, vertically downwards

Answer 1

The correct option is C $5km/h$, clockwise to vertical

$V_{Rain,Person}=V_{Rain}-V_{Person}=-4\hat{j}$ (vertically down)
Thus, $V_{Rain}-(-3\hat{i})=-4\hat{j}$ or, $V_{Rain}=3\hat{i}-4\hat{j}$
Thus, magnitude = $5km/h$, direction is in 4th quadrant, i.e. clockwise to vertical.