$A$ $150\, m$ long train is moving to the north at a speed of $10\, m/s$. $A$ parrot flying towards the south with a speed of $5\, m/s$ crosses the train. The time taken by the parrot to cross the train would be........$s$.

An aeroplane is to go along a straight line from $A$ to $B$,and back again. The relative speed with respect to wind is $V$. The wind blows perpendicular to the line $AB$ with speed $v$. The distance between $A$ and $B$ is $\ell$. The total time for the round trip is:

Two particles $A$ and $B$ are moving in a horizontal plane as shown in the figure at $t = 0$. The time after which $A$ will catch $B$ is.......$s$.

$A$ 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)?

$A$ river $200 \,m$ wide is flowing at a rate of $3.0 \,m/s$. $A$ boat is sailing at a velocity of $15 \,m/s$ with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank (in $\,m$)?

Two particles are moving along two long straight lines,in the same plane,with the same speed $= 20 \, cm/s$. The angle between the two lines is $60^{\circ}$,and their intersection point is $O$. At a certain moment,the two particles are located at distances $3 \, m$ and $4 \, m$ from $O$,and are moving towards $O$. Subsequently,the shortest distance between them will be