Final answer:
The coefficient of restitution for a ball dropped from 1 meter is calculated by taking the square root of the ratio of the rebound height to the original height. The coefficients are approximately 0.575, 0.761, and 0.387 for rebounds of 33 cm, 58 cm, and 15 cm, respectively.
Step-by-step explanation:
The coefficient of restitution (c) is defined as the square root of the ratio of the height to which a ball bounces (h) to the height from which it is dropped (H), represented by the formula c = (h/H)¹/². For a ball dropped from a height of 1 meter:
- If it bounces back up 33 cm, the coefficient is c = (0.33/1)¹/² ≈ 0.575.
- If it bounces back up 58 cm, the coefficient is c = (0.58/1)¹/² ≈ 0.761.
- If it bounces back up 15 cm, the coefficient is c = (0.15/1)¹/² ≈ 0.387.
This formula applies to idealized situations without air resistance and other losses.