The Prisoner

Jake is a prisoner of war who has been shot in the leg. He has noticed a break in the fence of the prison camp infirmary grounds. The grounds are 100 m by 100 m with a search light in the center. The beam of the light sweeps in a clockwise direction along the fence and walls of the building. It takes one minute for the light to make a complete sweep of the grounds. (i.e. The light is rotating at a constant rate of one turn per minute.) Jake is going to attempt to escape; he can only exit the building through door C and can only get out of the grounds through the break in the fence. Due to the leg injury, Jake can only run at a rate of 1.1 m/sec. Once he is at the break in the fence, he will need an additional 3 seconds to work his way through the break in the fence. Jake will also need to get at least 20 m beyond the fence in order to remain undetected by the light (i.e. The light beam has a 70 m radius). He can hide, without being detected by the light, inside doorways A and B. Can Jake make his escape? If so, what is his best route? You must use trigonometry in your solution. A diagram is included below.