When a ball is dropped from a height of 10 feet, it starts its journey towards the ground due to the force of gravity. Upon reaching the ground, it compresses slightly and then rebounds. However, it doesn’t return to its original height; instead, it bounces back to a fraction of the height from which it fell.
In the scenario presented, the ball rebounds to
34%
of its previous height after each bounce. To understand how high the ball bounces after each impact, let’s calculate it step by step:
- 1st Bounce: The ball is dropped from 10 feet. After hitting the ground for the first time, it bounces up to:
10 feet * 0.34 = 3.4 feet
- 2nd Bounce: After reaching 3.4 feet, the ball will again lose some height after hitting the ground:
3.4 feet * 0.34 ≈ 1.156 feet
- 3rd Bounce: Continuing this pattern, the ball will bounce from 1.156 feet:
1.156 feet * 0.34 ≈ 0.393 feet
As you can see, with each bounce, the height reaches a smaller and smaller value, and while it theoretically never fully comes to rest, in practical terms, it will eventually bounce so low that it can be considered to have stopped moving significantly.
The process illustrates the principles of energy loss due to factors like air resistance and the material properties of the ball. Each bounce represents a transformation of energy, predominantly from potential energy (when the ball is held at height) to kinetic energy (when it’s in motion) and back again, albeit with a fraction lost each time due to inelasticity and other real-world influences.