Q.3. A lifeguard, some feet up the beach, sees a drowning swimmer diagonally ahead,some distance offshore and some distance to one side, as shown in the Figure Q.3.The life guard can run at a certain speed and swim at a certain lesser speed. How does one find the fastest path to the drowning swimmer? This is a problem about finding the path of least time. The lifeguard travels faster on land than in water; the best path is a compromise as shown in Figure Q.3.

Assume that the lifeguard's running speed on the land is 8m/s while in the water is only2m/s. Assume that boundary between the sea and the land is the x axis. The initial position of the lifeguard in the x-y plane is assumed to be (0, 10), and the position of the drowning swimmer is (20, -20). Assume that the swimmer is drowning, in other words, the position of the swimmer is fixed in x-y plane. What is the shortest time that the lifeguard can reach the swimmer? What is the corresponding shortest path? You can use either calculus of variations or dynamic programming to solve this optimization problem.