student has a summer job as alifeguard at the beach. After spotting aswimmer in trouble

Chapter 4, Problem 14

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student has a summer job as alifeguard at the beach. After spotting aswimmer in trouble, he tries to deducethe path by which he can reach theswimmer in the shortest time. Thepath of shortest distance (path A) isobviously not the best since itmaximizes the time spent swimming(he can run faster than he can swim).Path B minimizes the time spent swimming but is probably not the best, sinceit is the longest (reasonable) path. Clearly the optimal path is somewhere inbetween paths A and B.Consider an intermediate path C and determine the time required to reach the swimmer in terms of the l1IDDing speed v,..,,. = 3 mls the swimming speedvswi = 1 mls; the distances L = 48 m, d. = 30m, and dw = 42 m; and thelateral distance y at which the lifeguard enters the water. Create a vector y thatranges between path A and path B (y = 20, 21, 22, ... , 48 m) and compute atime t for each y. Use MA1LAB built-in function min to find the minimumtime t.1, and the entry pointy for which it occms. Determine the angles thatcoJ.TeSpond to the calculated value of y and investigate whether your result satisfiesSnell's law of refraction:sin! = v,.llsina v,w1111