Bounce Height and Time II

From physics we know that the distance h that a ball falls in time t is h = (g / 2) t² where g = 9.8 m / s² is the acceleration due to gravity (constant for small heights if we ignore air friction). Thus h = 4.9 t² so t = (h / 4.9)^{1 / 2}. We just saw the relation of each bounce height to the first bounce height. The next mathlet shows how the time of each bounce is related to the time of the first bounce. As before, let h_n denote the height of the nth bounce, and now let t_n denote the time required for the ball to fall from that height.