Wind is blowing in the north direction at a 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 that the rain appears vertical to him?

Ship $A$ is sailing towards north-east with velocity $\vec{v}_A = 30\hat{i} + 50\hat{j}\,\text{km/hr}$,where $\hat{i}$ points east and $\hat{j}$ points north. Ship $B$ is at a distance of $80\,\text{km}$ east and $150\,\text{km}$ north of Ship $A$ and is sailing towards west at $10\,\text{km/hr}$. After how many hours will Ship $A$ be at the minimum distance from Ship $B$?

On a long horizontal belt,a child runs to and fro with a speed of $9\,km/h$ (with respect to the belt) between his father and mother located $50\,m$ apart on the moving belt. The belt moves with a speed of $4\,km/h.$ For an observer on the platform,the speed of the child in the direction of motion of the belt is.........$km/h$.

What do you mean by the term relative velocity?

$Assertion$ : The magnitude of velocity of two boats relative to the river is the same. Both boats start simultaneously from the same point on one bank and may reach the opposite bank simultaneously while moving along different paths.
$Reason$ : For boats to cross the river in the same time,the component of their velocity relative to the river in the direction normal to the flow should be the same.

$A$ boy is running on a plane road with velocity $v$ with a long hollow tube in his hand. The water is falling vertically downwards with velocity $u$. At what angle to the vertical,he must incline the tube so that the water drops enter it without touching its sides?