$A$ flag is mounted on a car moving due North with a velocity of $20 \, km/hr$. Strong winds are blowing due East with a velocity of $20 \, km/hr$. The flag will point in which direction?

Two cars, at a certain instant, are $50 \ km$ apart on a line running from south to north. The one farther north is moving west at $25 \ km/hr$. The other is moving towards north at $25 \ km/hr$. How long do they take to reach their distance of closest approach (in $min$)?

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 $B$?

The maximum speed of a boat in still water is $27 \,km/h$. Now this boat is moving downstream in a river flowing at $9 \,km/h$. $A$ man in the boat throws a ball vertically upwards with a speed of $10 \,m/s$. The range of the ball as observed by an observer at rest on the river bank is . . . . . . $cm$. (Take $g = 10 \,m/s^2$)

$A$ boat is sent across a river with a velocity of $8 \, km/hr$. If the resultant velocity of the boat is $10 \, km/hr$,then the velocity of the river is ........ $km/hr$.

$A$ river is flowing from $W$ to $E$ with a speed of $5 \, m/min$. $A$ man can swim in still water with a velocity of $10 \, m/min$. In which direction should the man swim to take the shortest possible path to reach the opposite bank (South)?