Mathematics

The key insight is that the ball travels both down and up, and each bounce reaches a predictable fraction of the previous height. After the initial drop, the ball bounces to $\frac{3}{4} \times 2$ m, then falls that distance, bounces to $\frac{3}{4}$ of that height, and so on—forming an infinite geometric series. You'll need to sum the distances for all downward and upward segments separately, then add them together.

The key insight is that the ball travels both down and up, and each bounce reaches a predictable fraction of the previous height. After the initial drop, the ball bounces to $\frac{3}{4} \times 2$ m, then falls that distance, bounces to $\frac{3}{4}$ of that height, and so on—forming an infinite geometric series. You'll need to sum the distances for all downward and upward segments separately, then add them together.