a ball rebounds one half of the height from which it was dropped. The ball is dropped from a height of 160 feet and keeps bouncing. what is the total vertical distance the ball will travel from the moment it is droppedto the moment it hits the floor for the fifth time?

1st bounce = 160 + 80

2nd bounce = 80 + 40
3rd bounce = 40 + 20
4th bounce = 20 + 10
5th (hit floor) = 10

Add these up to get your answer.

59

460

You toss a polybutadiene rubber ball 40 feet straight up from ground level. Each time it bounces, it rebounds 2/3 of the distance from which it fell. It continues bouncing indefinitely. How far does it travel before it comes to rest?

To find the total vertical distance the ball will travel from the moment it is dropped to the moment it hits the floor for the fifth time, we need to calculate the sum of the distances traveled during each bounce.

Given that the ball rebounds one-half of the height from which it was dropped, we can determine the distance traveled during each bounce.

Initially, the ball is dropped from a height of 160 feet, so the first bounce will reach a height of (1/2) * 160 = 80 feet. Since the ball has traveled twice the distance of the first bounce when it completes its descent, the total distance after the first bounce is 160 + 80 = 240 feet.

For the second bounce, the ball will reach a height of (1/2) * 80 = 40 feet. Adding this distance to the previous total, we get 240 + 40 = 280 feet.

The third bounce will reach a height of (1/2) * 40 = 20 feet. Adding this distance to the previous total, we get 280 + 20 = 300 feet.

Similarly, for the fourth bounce, the ball will reach a height of (1/2) * 20 = 10 feet. Adding this distance to the previous total, we get 300 + 10 = 310 feet.

Finally, for the fifth bounce, the ball will reach a height of (1/2) * 10 = 5 feet. Adding this distance to the previous total, we get 310 + 5 = 315 feet.

Therefore, the total vertical distance traveled by the ball from the moment it is dropped until it hits the floor for the fifth time is 315 feet.