Reflections on the Woolwich Ferry

Extract

A ferry starting on one side of a river is to cross to the adjacent point on the opposite bank travelling at a constant speed f but moving against a variable river sneed We will ignore starting and stonninc difficulties which only operate for a short interval of time. The ferry moves so that it is always aiming at the target position T. The river is assumed to be straight and the speed of the river is given by the function r(x) which is non-negative, continuous and differentiable for 0 ≤ x ≤ a, where a is the width of the river. We shall show that the solution reduces to two integrations and the condition which determines whetIer the derry can reach its destination will be given.