$A$ ship $A$ is moving Westwards with a speed of $10 \, km \, h^{-1}$ and a ship $B$,$100 \, km$ South of $A$,is moving Northwards with a speed of $10 \, km \, h^{-1}$. The time after which the distance between them becomes shortest is ........ $hr$.

$A$ train of $150 \ m$ length is going towards the north direction at a speed of $10 \ m/s$. $A$ parrot flies at a speed of $5 \ m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is........$s$.

On a long horizontally moving belt,a child runs to and fro with a speed $9 \; km \; h^{-1}$ (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 $4 \; km \; h^{-1}$. For an observer on a stationary platform outside,what is the:
$(a)$ speed of the child running in the direction of motion of the belt?
$(b)$ speed of the child running opposite to the direction of motion of the belt?
$(c)$ time taken by the child in $(a)$ and $(b)$?
Which of the answers alter if motion is viewed by one of the parents?

Rain is falling vertically with a speed of $30\,ms^{-1}$. $A$ woman rides a bicycle with a speed of $12\,ms^{-1}$ in the east to west direction. She should hold her umbrella:

$A$ steam boat goes across a lake and comes back: $(i)$ on a quiet day when the water is still and $(ii)$ on a rough day when there is a uniform current so as to help the journey onward and to impede the journey back. If the speed of the launch,on both days,was same,the time required for the complete journey on the rough day as compared to that on the quiet day,will be

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 $min$)?