Phooey. I don't think my description was very enticing. Here's a more specific question. In the linked image below, what is the relationship between lengths a, b, c and d? http://www.flickr.com/photos/70917169@N02/6416169329/in/photostream I've googled around a bit.. haven't found anything on using a parabola on its side to trace out the pattern of multiple bounces. Any suggestions would be very much appreciated. Best, Gary On Sun, Nov 27, 2011 at 3:06 PM, Gary Antonick <gantonick@post.harvard.edu>wrote:
Hi all,
I happened to notice something interesting about parabolas several months ago. Am wondering if it would make a good puzzle.
It's about a ball bouncing up an incline.
Say you point a cannon at 45° and fire. A cannonball flies out and hits a perfect reflector at the same height as the mouth of the cannon. If the cannonball bounces once on the reflector and then returns along its original path to the mouth of the cannon you'd know the reflector was at 45 °.
But what if the ball bounces 5 times? What's the angle of the reflector? And - a related question - what trajectory does the bouncing ball take?
All frictionless, of course, and w/o air resistance. And no calculus (or formulas of any kind) required.
- Gary