Question

Consider throwing a basketball straight up from a height of six feet while standing on a flat surface. If the ball reaches a height of 15 feet, and the ball rebounds from each bounce to a point 90% as high as its previous height, find the total distance that the ball travels (up and down) before coming to rest.

Answer 1

The total distance that the ball travels before coming to rest is 18 feet.

Step-by-step explanation:

To find the total distance that the basketball travels before coming to rest, we need to consider the height at each bounce as well as the number of bounces. Given that the ball rebounds to 90% of its previous height, we can determine the number of bounces by repeatedly dividing the final height (15 feet) by 0.9 until we reach the initial height (6 feet). In this case, there are 2 bounces.

Therefore, the distance traveled by the ball can be calculated as follows:

1. First bounce: 15 - 6 = 9 feet
2. Second bounce: 9 - 6 = 3 feet
3. Initial throw: 6 feet

The total distance the ball travels before coming to rest is 9 feet (first bounce) + 3 feet (second bounce) + 6 feet (initial throw) = 18 feet.