Answer:
i) [tex]h = H \cdot 3^{-n}[/tex], ii) [tex]s = H\cdot (1 + 2\cdot \Sigma_{i = 1}^{n} 3^{-i})[/tex]
Explanation:
i) After each bounce, two thirds of previous energy is lost by the ball. Then, the height observes a geometric progression which is described herein:
[tex]h = H\cdot \frac{1}{3^{n}}[/tex]
[tex]h = H \cdot 3^{-n}[/tex]
Where n is the number of bounces.
ii) The total vertical distance that ball travels before coming to rest is:
[tex]s = H + 2\cdot H \cdot \Sigma_{i = 1}^{n} \cdot 3^{-i}[/tex]
[tex]s = H\cdot (1 + 2\cdot \Sigma_{i = 1}^{n} 3^{-i})[/tex]
