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.)

I'm not sure I remember my Calculus correctly, but I decided to try to determine the slope of the path taken by the ball at the point it strikes the inclined plane.

y' = -x/9 at x=6 gives y' = -2/3.

So, it doesn't look like the ball bounces back on the same path, because the slope of the derivative isn't -2 (the negative reciprocal of the slope of the inclined plane).

I'm not sure where to go from here (or even if I stayed on the right path to get here) but I guess the ball would bounce straight up (based on the slope of the path at the point of impact reflected about a line perpendicular to the inclined plane) and come straight down and hit point (6,3) again before it continues on to (-7.5, -15).

Ok, mathematicians.  Comment so that I can learn.