The Best Bouncing Ball Geometric Series References
The Best Bouncing Ball Geometric Series References. I applied geometric series $${ \sum_{i=0}^\infty {36\times\left( \frac{2}{3} \right)^i } = 108}$$ This will lead to summing a geometric series, but let us first investigate, what happens to a ball being dropped from a height h.
Say we have an infinite geometric series whose first term is and common ratio is. (a) sketch the ball's vertical travel for several bounces. A rubber ball was dropped from a height of 36m.
Bouncing Balls And Geometric Series, Robert Styer And Morgan Besson.
The height of each bounce is a fraction of the height of the previous bounce. And each time its strikes the ground it rebounds to a height of 2/3 from which it last fell. A golf ball or a super ball bounces rather nicely;
Geometric Sequences And Series P.
Vertical is ball height, horizontal is bounce. Suppose this ball is dropped from a height of 10 feet above the floor. A bouncing ball is one of the simplest models that shows the zeno phenomenon.
Answer According To Reviewer Is 180M.
On the next page, we find the sum of a geometric series by the. The bouncing ball geometric series is a nice example related to zeno's paradoxes that forces students to think about how infinitely many discrete steps can sum to a finite answer. Practice this lesson yourself on khanacademy.org right now:
Zeno Behavior Is Informally Characterized By An Infinite Number Of Events Occurring In A Finite Time Interval For Certain Hybrid Systems.
For instance, suppose we drop a golf ball from a height of 64 centimeters. If is between and (i.e. On the second rebound the height the ball reaches is ⅗⋅6=18/5;
Bouncing Balls And Geometric Series, Robert Styer And Morgan Besson.
Here and are initial conditions for position and velocity. It explains how to use geometric series to find the total distance of the bouncing ball. This lesson explains the good old bouncing ball problem.