The speed of a swimmer in still water is $20 \; m/s$. The speed of river water is $10 \; m/s$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path,the angle at which he should make his strokes with respect to north is given by ......$^o$ west.

$A$ 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

Two trains,each of length $100 \, m$,are moving parallel towards each other at speeds of $72 \, km/h$ and $36 \, km/h$ respectively. In how much time will they cross each other (in $, s$)?

$A$ person climbs up a stalled escalator in $60\,s$. If standing on the same but escalator running with constant velocity,he takes $40\,s$. How much time is taken by the person to walk up the moving escalator?........$s$

$A$ boat takes $2 \, h$ to travel $8 \, km$ and back in still water. If the velocity of water is $4 \, km/h$,the time taken for going upstream $8 \, km$ and coming back is:

$A$ swimmer can swim in still water with speed $v$ and the river is flowing with velocity $v/2$. To cross the river in the shortest distance,the swimmer should swim at an angle $\theta$ with the upstream. What is the ratio of the time taken to swim across in the shortest time to the time taken to swim across the shortest distance?