Why isn't the spiral a bit of an S?

It seems the rabbit would have to begin and end the mad dash at 90º angles. At the beginning the rabbit would have to take an initial stroke directly away from the agent so the agent doesn't change direction. The very end of the spiral would run parallel to the shore so it seems the very last stroke of the rabbit would be directly into shore.

A spiral shape must take care of this but I don't know how to show it.