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Experimentsâ€‹

Bounce Back – The Pattern of Rebound Heights

Experiment #18 from Real-World Math with Vernier

Education Level
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

$y = h{p^x}$

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)pÂ =Â 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 experiment features the following sensors and equipment. Additional equipment may be required.

Motion Detector

CBR 2