A lion and a lion tamer are enclosed within a circular cage. If they move at the same speed but are both restricted by the cage, can the lion catch the lion tamer? (Represent the cage by a circle, and the lion and lion tamer as two point masses within it.)

I say yes and here is my strategy for how the lion can catch the tamer.  First, the lion moves to the center of the cage.  Now express the tamer's position in the cage in polar format, using the center as the origin.  How the tamer's motion in the cage can be seen as changes in the radius and angle component of his position.  Now once the lion is in the center of the cage then there are two possibilities, either the tamer is there as well in which case he is caught, or he is somewhere else in the cage and the tamer's radius is larger than the lions which is zero.  As a result of this, no mater how the tamer moves the lion we be able to match the tamer's change in angle, and use whatever portion of it's absolute velocity is left to effect a change in it's radius.  Using this strategy, the tamer could prevent the lion from getting closer by running towards the cage call directly away from the lion, however the tamer will eventually reach the cage wall in which case the lion, using this strategy, is now able to guarantee that the distance between the lion and tamer will always decrease and thus the lion will eventually catch the tamer.

Posted by Daniel on 2013-06-10 17:50:23