Saturday, July 2, 2011

The Ant On An Elastic Rope

An ant starts to walk along an elastic rope which is 1 km long, at a speed of 1 cm per second (relative to the rope it is crawling on). While this happens the rope is uniformly stretched by 1 km per second (i.e. after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc.). Assume the rope will never break and we have an infinite amount of time on our hands. Will the ant ever reach the end of the rope?

Here's a hint: Yes, yes it will.