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

Horizontal component of rain's velocity will be equal to velocity of wind which is 2 m/s in north direction. If cyclist goes towards north with velocity 2 m/s, then w.r.t. him rain's horizontal component of velocity will be zero, and he will See only vertical component.