Swimming across a canal

γ= degrees


show trajectory?

  • swimmer

  • starting point

  • flotsam

  • ladder

  • ladder

What is this?

A canal has uniform flow towards the right, with velocity v. (This flow is made apparent by the piece of "flotsam" depicted on the surface.) A swimmer is able to swim with constant velocity w, relative to the water. A ladder is displaced a distance D from the point directly opposite. Positive D is downstream. The width of the channel is L. In this physlet, the ladders are fixed at D=-L and D=L.

At what angle γ should the swimmer align his or her body so that the straight-line trajectory ends exactly at a designated ladder at the opposite shore? Let γ be measured counterclockwise, with γ=0 to the right.

First consider v/w=1.2. This means the speed of the water (relative to shore) is faster than the speed of the swimmer (relative to the water). Find two solutions for γ that allow the swimmer to reach the downstream ladder.

Next consider v/w=0.8; the swimmer is thus able to swim upstream. Find the values of γ that allow the swimmer to reach the upstream and downstream ladder.