[math-fun] parabola puzzle

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