A mathematician stands on a beach with his dog at point A. He throws a tennis ball so that it hits the water at point B. The dog, wanting to get the tennis ball as quickly as possible, runs along the straight beach to point D and then swims from D to point B to retrieve his ball. Assume C is the closest point of the edge of the beach to the tennis ball (see figure). B (a) Assume the dog runs at speed r and swims at speed s, where r > s and both are measured in meters/second. Also assume the lengths of BC, CD, and AC are r, y, and z respectively. Find a function T(y) representing the total time it takes for the dog to get the ball. (b) Verify that the value of y that minimizes the time it takes to retrieve the ball is y = Vr/s+1Vr/s –1 (c) If the dog runs at 8m/s and swims at 1m/s, what ratio 2 produces the fastest retrieving time?

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