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Bounce Back - The Pattern of Rebound Heights

Figure from experiment 18 from Real-World Math with Vernier


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. It’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.


  • 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 »

Activity 18 from Real-World Math with Vernier Lab Book

<i>Real-World Math with Vernier</i> book cover

Included in the Lab Book

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

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