A man is standing on a rock in the middle of a circular lake of radius 1. There is a tiger on the shore of the lake that can run four times as fast you can swim, however the tiger can not swim. The tiger is hungry and always attempts to keep the distance between the two of you at a minimum.
How can you safely swim to shore?
So long as the man is less than 1/4 of the radius of the circle from the center (the ratio of the speeds) he can keep the tiger opposite himself with regard to the lake and still have a component of motion left over to go outward from the center. Once he reaches 1/4 the radius out, he can no longer do this, but at that point with only 3/4 the radius to go, the tiger has to travel pi times the radius to get to the nearest point. The tiger's speed being 4 times the man's, this is covered in pi/4 times the time it takes the man to go one radius of distance, which is more than the 3/4 that the man takes.
I don't know if it would help if the man applied some component of his motion nonradially once the 1/4 point was reached, or if he should just head straight for shore at that point and depend on the (pi3)/4 time unit advantage.

Posted by Charlie
on 20031029 16:09:12 