A student has a summer job as a lifeguard at the beach. After spotting a swimmer in trouble, he tries to deduce the path by which he can reach the swimmer in the shortest time. The path of shortest distance (path A) is obviously not the best since it maximizes 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, since it is the longest (reasonable) path. Clearly the optimal path is somewhere in between paths A and B.

Consider an intermediate path C and determine the time required to reach the swimmer in terms of the l1IDDing speed vrun. = 3 mls the swimming speed vswi = 1 mls; the distances L = 48 m, d. = 30m, and dw = 42 m; and the lateral distance y at which the lifeguard enters the water. Create a vector y that ranges between path A and path B (y = 20, 21, 22, ... , 48 m) and compute a time t for each y. Use MA1LAB built-in function min to find the minimum time tmin, and the entry pointy for which it occms. Determine the angles that correspond to the calculated value of y and investigate whether your result satisfies Snell's law of refraction:
sinɸ/sina = vrun/vswim

dw ds swimmer Lifeguard shorelinc