Vernier Software & Technology

# Bounce Back - The Pattern of Rebound Heights

## 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

$y = h{p^x}$

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 = hp2, and so forth. The relation above is generalized for any x number of bounces.

In this exercise, you will collect motion data for a bouncing ball using a Motion Detector. You will then analyze this data to test the model y = hpx.

## Objectives

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

## Sensors and Equipment

This activity requires each of the following Vernier sensors and equipment (unless otherwise noted):

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

The student-version preview includes:

• Step-by-step instructions for computer-based data collection
• List of materials and equipment

Note: The experiment preview of the computer edition does not include essential teacher information, safety tips, or sample data. Instructions for Logger Pro and other software (such as LabQuest App or TI handheld software, where available) are on the CD that accompanies the book. We strongly recommend that you purchase the book before performing experiments.

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### Activity 18 from Real-World Math with Vernier Lab Book

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#### Included in the Lab Book

Vernier lab books include a CD with word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.