**ERIC Number:**EJ902125

**Record Type:**Journal

**Publication Date:**2010-Oct

**Pages:**7

**Abstractor:**ERIC

**Reference Count:**3

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Exploring the Mathematics of Bouncing Balls

Vinogradova, Natalya; Blaine, Larry G.

Mathematics Teacher, v104 n3 p192-198 Oct 2010

A common textbook problem asks students to calculate the total distance traveled by a bouncing ball, from its initial release until it comes to rest, under the assumption that the height of each bounce is some fixed proportion "r" of the height of the previous bounce. The solution is found by inserting information about "r" and the height from which the ball was dropped into a formula for an infinite geometric sum. In this article, the authors discuss some variations on this general idea, involving measurements of times--rather than heights--for various combinations of bounces. They present an activity that allows students to explore geometric sums and quadratic equations and analyze experimental data using simple equipment--stopwatches, tape measures, and golf balls. The activity can be carried out in any classroom and can be used to illuminate different mathematical topics, such as statistical analysis of data, geometric sequences in general, and the sum of decreasing geometric sequences in particular. Students see mathematics as a useful tool for creating and analyzing models that describe real processes. (Contains 3 tables.)

Descriptors: Statistical Analysis, Geometric Concepts, Motion, Physics, Mathematical Concepts, Mathematics Instruction, Computation, Equations (Mathematics), Learning Activities, Measurement Techniques, Teaching Methods

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A