Question

A ball is dropped from a height of 16 m. After each bounce the ball rises to 75% of its previous height. Determine the total vertical distance the ball has traveled when it bounced for the 10 th time. Select one: a. 104.79 m b. 88.12 m c. 120.79 m d. 61.30 m

Answer 1

b. 88.12 m The total distance traveled after the first bounce is the sum of the descent (16 meters) and the rise (12 meters), giving us a total of 28 meters.

Step-by-step explanation:

The total vertical distance traveled by the ball after the 10th bounce is 88.12 meters. This is calculated by adding the descending and ascending distances covered by the ball after each bounce.

In this scenario, the ball is dropped from a height of 16 meters. After the first bounce, it rises to 75% of its previous height (16 * 0.75 = 12 meters). The total distance traveled after the first bounce is the sum of the descent (16 meters) and the rise (12 meters), giving us a total of 28 meters.

For subsequent bounces, the ball continues this pattern: descending from the previous height and then rising to 75% of the previous height. After each bounce, the total distance traveled can be calculated by adding the descent and rise distances. By iteratively computing this for 10 bounces, the cumulative vertical distance traveled by the ball amounts to 88.12 meters.

The calculation considers both the initial descent and the subsequent rises and descents, leading to the conclusion that after the 10th bounce, the ball has covered a total vertical distance of 88.12 meters.

Answer 2

To find the total vertical distance the ball has traveled after bouncing for the 10th time, we need to calculate the distance traveled during each bounce and sum them up.

Step-by-step explanation:

To find the total vertical distance the ball has traveled after bouncing for the 10th time, we need to calculate the distance traveled during each bounce. The ball rises to 75% of its previous height after each bounce. So, the distance during each bounce can be calculated as 16 m + 0.75 * 16 m + (0.75 * 0.75) * 16 m + ... n times.

To find the total vertical distance after the 10th bounce, we need to sum up the distance traveled during each bounce up to the 10th bounce. This can be calculated using the formula for the sum of a geometric series:

Total vertical distance = first term * (1 - r^10) / (1 - r)

Plugging in the values, the total vertical distance traveled by the ball after bouncing for the 10th time is approximately 104.79 m.