A man stands in the center of a circular field which is encompassed by a narrow ring of water. In the water there is a shark which is swimming four times as fast as the man is running. Can the man escape the field and get past the water to safety?
Yes, he can. Let the radius of the field is R and its center I. First the man should start running along a circle with center I and radius slightly less than R/4. His angular speed will be larger than the angular speed of the shark, so he can keep running until gets opposite to it with respect to I. Then, the man should dash away (in a straight line) towards the water. Since he will need to cover approximately 3R/4 distance and the shark will have to cover approximately 3.14R distance, the man will have enough time to escape.