Bouncing Ball A certain ball rebounds to half the height for which it is dropped. Use an infinite geometric series to approximate the total distance the ball travels after being dropped from above the ground until it comes to the rest.
The total distance that the ball travels.
The ball bounces to half the height form which it is dropped.
The sum of the infinite geometric series is given by .
When the ball hits the ground for the first time, it has traveled a distance and the distance traveled up and down for the second time is , it will travel twice when up and down and similarly, it will be the half of the previous distance for further bounces.
Form a sequence-
The total distance for infinite times, written as-
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started