Part 2: Super-ball

A small ball is thrown toward an incline. This (amazing) ball bounces perfectly.
It is thrown to the right horizontally from the point (0,5) and follows the path of the parabolic equation y=5 - (x^2)/18.
The incline follows the equation y=x/2.

Find the equation of the path the ball takes after its first bounce off of the incline.

(If you wish, find some of the subsequent bounces.)
(Assume that gravity pulls straight down on the ball. Also assume the ball is not spinning so that it is perfectly reflected.)

The ball strikes the inclined plane at the point (6,3).  This is easily determined by substitution of y= x/2 into the equation y=5 - (x²)/18, then solving the quadratic equation.  The other solution to the quadratic equation is (-7.5, -15), which is where the ball would bounce to if it were reflected back on the original path.  But is it?

Posted by Mindrod on 2006-02-10 21:48:22