Factors Affecting Bounce Height:
* Coefficient of Restitution (COR): This is the most important factor. It represents the ball's ability to bounce back. A higher COR means a larger percentage of energy is returned during the bounce, leading to a higher bounce height. Different materials have different CORs (e.g., a rubber ball has a higher COR than a clay ball).
* Drop Height: As the drop height increases, the ball has more time to accelerate under gravity, resulting in a greater impact velocity. This generally leads to a higher bounce height.
* Air Resistance: Air resistance plays a role, particularly at higher drop heights. It slows the ball down both during the descent and ascent, reducing the bounce height.
* Surface Properties: The surface the ball bounces on also influences the bounce height. A hard, smooth surface generally leads to a higher bounce than a soft or rough surface.
Relationship:
* Not Perfectly Linear: While the bounce height generally increases with the drop height, the relationship isn't linear. The bounce height will increase at a decreasing rate as the drop height increases. This is because the energy loss during the bounce (due to factors like heat and sound) becomes more significant at higher drop heights.
* Empirical Formula: You can approximate the relationship using an empirical formula:
```
Bounce Height = COR² * Drop Height
```
This formula assumes a constant COR and negligible air resistance.
Example:
If a ball has a COR of 0.8 and is dropped from a height of 1 meter:
* Bounce Height = 0.8² * 1 meter = 0.64 meters
Conclusion:
The bounce height of a ball is directly related to the drop height, with a higher drop generally leading to a higher bounce. However, the relationship is not perfectly linear and is influenced by various factors like the ball's material, air resistance, and the surface properties.