# Bounce Back - The Pattern of Rebound Heights

Recommended for High School.

## Introduction

When a ball bounces up and down on a flat surface, the maximum height it reaches decreases from bounce to bounce. In fact, the maximum height decreases in a very predictable way for most types of balls. The relationship between the maximum height attained by the ball on a given bounce (which we will call the *rebound height*) and number of bounces that have occurred since the ball was released is an exponential

where *y* represents the rebound height, *x* represents the bounce number, *h* is the release height, and* p* is a constant that depends on the physical characteristics of the ball used. Itâ€™s easy to see where this model comes from: Suppose that the ball is released from height *h*. Then on each bounce it rebounds to a fraction *p* of the previous maximum height. After zero, one and two bounces, the ball will attain a maximum height of *h*, *hp*, (*hp*)*p* = *hp*^{2}, and so forth. The relation above is generalized for any *x* number of bounces.

*y*=

*hp*

^{x}.

## Objectives

- Record the successive maximum heights for a bouncing ball.
- Model the bounce height data with an exponential function.

## Sensors and Equipment

This activity features the following Vernier sensors and equipment.

### Option 1

### Option 2

### Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

## Standards Correlations

See all standards correlations for *Real-World Math with Vernier* »

*Real-World Math with Vernier*

*Real-World Math with Vernier*

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