Minimal Path Generalization Problem: A swimmer is at a distance p, in feet, from the

Chapter 10, Problem 6

(choose chapter or problem)

Minimal Path Generalization Problem: A swimmer is at a distance p, in feet, from the beach. His towel is at the waters edge, at a distance k, in feet, along the beach (Figure 10-4j). He swims at an angle to a line perpendicular to the beach and reaches land at a distance x, in feet, from the point on the beach that was originally closest to him. He can swim at velocity s, in feet per minute, and walk at velocity w, in feet per minute, where s < w. Prove that his total time is a minimum if the sine of the angle the slant path makes with the perpendicular equals the ratio of the two speeds. That is, prove this property: Figure 10-4j