Time to pull in the big guns. This is a frustrating twist on a classic problem:
A cop is chasing a burglar, both running east along an east-west shore line. (The water is to the north; land is to the south.) When the cop is 50m behind him, the burglar jumps into the water and begins swimming in a straight line 30 degrees north of the shore (a bearing of 60 degrees from North). The burglar swims at a rate of 2m/s. The cop runs along the shore for a short time, then jumps in the water and swims in a straight line on a course that will intercept the burglar. The cop can run 5m/s along the shore, and can swim at a rate of 3m/s. How many meters should the cop run before jumping in the water in order to apprehend the burglar in the shortest amount of time? At what angle from the shore should he turn?
I can get as far as drawing a picture, and coming up with times for three specific points along the shore. Creating a general equation to optimize, though, has me stumped. Any help would be appreciated.