$A$ river is flowing from west to east at a speed of $8\,m/min$. $A$ man on the south bank of the river,capable of swimming at $20\,m/min$ in still water,wants to swim across the river in the shortest time. He should swim in a direction

$A$ man can swim with a speed of $4 \ km/h$ in still water. How long does he take to cross a river $1 \ km$ wide, if the river flows steadily at $3 \ km/h$ and he makes his strokes normal to the river current (in $min$)?

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.........$km/h$.

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of $B$ with respect to $A$?

$A$ river of width $200 \ m$ is flowing from west to east with a speed of $18 \ km/h$. $A$ boat, moving with a speed of $36 \ km/h$ in still water, is made to travel one round trip (bank to bank of the river). The minimum time taken by the boat for this journey and the displacement along the river bank are . . . . . . and . . . . . . respectively.

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54\; km\; h^{-1},$ and train $B$ moves south with a speed of $90\; km\; h^{-1}.$ What is the velocity (in $m\; s^{-1}$) of a monkey running on the roof of the train $A$ against its motion (with a velocity of $18\; km\; h^{-1}$ with respect to the train $A$) as observed by a man standing on the ground?