A canal of width 2a has parallel straight banks and the water flows due north . The points A and B are on opposite banks and B is due east of A , with the point O as the midpoint of AB . THe x-axis and y-axis are taken in the east and north directions respectively with O as the origin . The speed of the current in the canal ,

, where

is the speed of the current in the middle of the canal and x the distance eastwards from the middle of the canal . A swimmer swims from A towards the east at speed

, relative to the current in the canal . Taking y to denote the distance northwards travelled by the swimmer , show that