Question

Wind is blowing in the north direction at a speed of $2m/s$ which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the horizontal component of rain appears $2m/s$ south to him?

• A. $2m/s$ south
• B. $2m/s$ north
• C. $4m/s$ north
• D. $4m/s$ south

Answer 1

The correct option is C $4m/s$ north

$V_{Rain,Cyclist}=V_{Rain}-V_{Cyclist}=-2\hat{i}$ (taking north as $+\hat{i}$)
Thus, $\left(2\hat{i}\right)-V_{Cyclist}=-2\hat{i}$ or, $V_{Cyclist}=2\hat{i}+2\hat{i}=4\hat{i}$
Thus, magnitude = $4m/s$, direction is in $+\hat{i}$, i.e North.