Reflections on a Bouncing Ball

While observing the bounce heights of various kinds of sports balls dropped from different heights onto a variety of surfaces, we thought of the following question: Could measurements of drop and bounce heights of balls of different diameters, but of the same material, falling from different heights, but on the same surface, be expressed by a simple mathematical formula? Our objective was to provide a simple classroom ball-drop experiment that produced robust and interesting data sets from which students could address this question. With a suitable choice of variables, all the ball drop data could be collapsed to a single curve, so that given the mass and drop height of the ball, the bounce height could be reasonably estimated (±10% of measured values).