Challenge problem: Forest Gump is standing on the shore of a circular lake of radius R. Jenny is in a boat in the center of the lake. Forest can run 4 times as fast as Jenny can row. Forest is trying to meet Jenny on shore. Can Jenny avoid him and still get to shore? Assume that our contestants are intelligent enough to pursue optimal strategies.
Challenge problem ("due" Monday): How far away from the center of the lake can Jenny get and still keep the center of the lake between herself and Forest? Show that she can get as close as she wants to this maximum distance by deriving and solving a differential equation. (HINT: Use polar coordinates.)