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?

Well have you all heard of that calculus problem involving three motocyclist.Well here it is.

There are 3 motor cyclist each at the vertex of an equilateral triangle.A moves towards B,B towards C and C towards A.They all are at equal speeds.Where shall they meet?

Most of you would say that they would never meet, but they would and meet at the centriod.This solution is according to calculus.I think similar ideas work in this problem.

The start moving in a direction opposite to the tiger.The tiger too starts running towards the man.After swimming for time t(infinitely small) he changes his direction and swims oppsite to the tigers current postion.

Thus his path would be an arc.This is my solution.

Posted by Sandeep on 2003-11-03 11:53:42