A river d km wide is flowing at the rate A swimmer which can swim with velocity relative to water wants to cross the river straight across. Find how long will he take to cross the river?
The path AB is the shortest path to cross the river.
To cross the river straight across along path AB, the resultant velocity of swimmer and the water flow should be along AB i.e. perpendicular to the direction of water flow.
To meet this condition, let the swimmer start swimming upstream at angle 0 with AB.
Time taken by the swimmer to cross the river is,