All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
Bumper Cars (Posted on 2004-12-30) Difficulty: 3 of 5
Some bumper cars are moving around a circular track at the same constant speed. However, they are not all going in the same direction. Collisions are perfectly elastic, so that two colliding cars instantaneously change directions (and continue at the same speed).

Show that at some point in the future, all the cars will be back to their starting positions and directions. Assume that each car has no length.

See The Solution Submitted by David Shin    
Rating: 2.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 14
Imagine that instead of elastic collisions, the cars passed right through each other to continue their journey.  Since they are all going at the same speed, one revolution later each car would be at its original starting point going the same direction (since in this altered problem the cars never change direction).

So clearly there will be infinite times, at one period intervals where the above conditions will be true.

But with collisions, (the problem as described) we don't know which car will be where.  We do know that the order of the cars will always be the same, since they never pass each other.  So once N periods have gone by, there should be at least one time when each car was at its original starting location.
  Posted by Larry on 2004-12-30 18:12:07
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (2)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information