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?

Sorry, Brian, but tigers don't sleep at night: that's when they hunt. Swim at dawn, after the hunt but before the awakening. Now: I like the idea of swimming underwater, but you'll have to remember we ain't in Cleveland if we have a rock in a body of water with a radius (period...) of 1.

The lack of distance measures shouldn't bother me, though it does. Mathematically, if Tiger moves at 4x Man speed, there's no big bother about units. Still and all, there's a major difference between 1 inch and 1 mile.

Let's go with 1 Km. (x) as the distance to the shore. The average human swims probably at 2/3 the speed of the fastest human (at 2.29 m/s:see http://hypertextbook.com/facts/2000/NoahKalkstein.shtml), which would yield about 1.53 m/s. It would then take 7min. for an average human to swim one Km (called x/y). The body of water (now BOW) will be (pi)x around. Derivatively, the tiger covers about 6.12 m/s, and would be across the lake 52.8 seconds before the human gets there. The logarithmic spiral proposed by several earlier seems to be the best answer.

Posted by Choop on 2003-11-03 01:49:36