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?
(In reply to
Specifically... by Charlie)
Well stated, Charlie.
I was playing with some numbers/equations, and the calculus was getting too complicated for me to do this over a break at work, but I think here's a 'smooth' path for the man to follow, that I believe will get him there ahead of the tiger.
First the man gets on the 'East' side of the rock (let's say where theta, the radian angle = 0 or 2ð), then let the man traverse the path that is described by:
for:
7/8 * π ≤ theta ≤ 11/8 * π,
let r = (4 / π²) * (theta - (7/8)*π)²
where r is the distance from the center of the lake, and theta is the angle from East in radians.
Would anyone like to verify this?
Edited on October 29, 2003, 4:26 pm
re: Specifically...
