Using calculus to model movement of an object

[musicgold]

Hi,

I am trying to use calculus to analyze the following puzzle. I already know the answer to the puzzle -200Km.
What I want to be able to do is to model or calculate distance the fly travels in a particular sweep. See the attached Excel file to better understand what I mean.

I feel that Calculus might help me in modeling the movement of the fly, but not sure. How should I go about doing this?

Puzzle:
Two trains are 200 km apart, and traveling towards each other at 100 km/hour each. From train A a fly takes off, flying straight above the rails to train B at the speed of 200km/hour, bounces off it and flies back to train A. This is repeated till the trains crash together and the fly is smashed. How much distance does the fly cover?


Thanks.

 

[Filip Larsen]

There are, as you may be aware of, several ways to solve this puzzle.

Spoiler

http://thesciencepundit.blogspot.com/2006/07/john-von-neumann-and-mathematicians.html

 

[musicgold]

Thanks a lot Filip.

That is exactly what I was looking for!