You are starting a race on the beach at point A to reach a buoy at point B in the ocean, as pictured below (bird's eye view). A=(0,0) x Beach Ocean B = (b1, b2) You can run along the beach twice as fast as you can swim in the ocean. The aim is to find that the optimal location x to enter the ocean is such that 0 = 30. (a) Let v = running speed and v = swimming speed. Show that the total travel time between A and B is (explain your working): 1 T(x) = VI x+ 1 v (b x) + b. (b) Calculate T'(x). (c) Show that if v = 2v2, the optimal angle to enter the ocean is 0 = 30. Hint: Note that T(x) has no maximum (you can take arbitrary long detours) and that sin 0 (b-x) (bi-x)+b