Question

With each successive bounce, new tennis balls bounce to about 53% of the previous bounce height when dropped on a hard surface. if byron drops a tennis ball from a height of 10 feet, how high will the ball go on the fifth bounce? what is the explicit formula that shows how high the tennis ball will be on the nth bounce? a) Approximately 1.9 feet

b) Approximately 3.18 feet
c) Approximately 5.35 feet
d) Approximately 8.98 feet

Answer 1

Using the geometric series formula to find the height of the tennis ball on the fifth bounce after being dropped from a 10-foot height with 53% retention each bounce, the ball would bounce approximately 7.87 feet on the fifth bounce, which does not match any of the provided answer choices.

Step-by-step explanation:

The question asks for the height of a tennis ball on the fifth bounce, given that it loses a certain percentage of height on each successive bounce. The initial height from which the ball is dropped is 10 feet, and with each bounce, it reaches 53% of the height of the previous bounce.

To calculate the height on the fifth bounce, we can use the formula for a geometric series:

heightn = initial height × (bounce factor)(n-1)

Where the bounce factor is 0.53 for a 53% bounce height retention. So for the fifth bounce (n=5), the formula becomes:

height5 = 10 × (0.53)(5-1)

height5 = 10 × (0.53)4

height5 = 10 × 0.078765

height5 ≈ 0.78765 × 10 ≈ 7.8765 feet (approximately)

This means the correct answer would be about half of option c, which is approximately 5.35 feet rounded, and matches no provided answer choice exactly.