We will be closed on August 21 to allow our employees to enjoy the Great American Eclipse.

Vernier Software and Technology
Vernier Software & Technology

That's the Way the Ball Bounces - Height and Time for a Bouncing Ball

Figure from experiment 10 from Real-World Math with Vernier

Introduction

Picture a bouncing ball. Between impacts with the floor, the ball rises and slows, then descends and speeds up. For any particular bounce, if the ball’s height is plotted as a function of time, the resulting graph has a parabolic shape. In other words, the relationship between height and time for a single bounce of a ball is quadratic. This relationship is expressed mathematically as

y = a{x^2} + bx + c

where y represents the ball’s height at any given time x. Another form of a quadratic equation is

y = {a{(x - h)^2} + k}

where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and a is a parameter. This way of writing a quadratic is called the vertex form.

In this activity, you will record the motion of a bouncing ball using a Motion Detector. You will then analyze the collected data and model the variations in the ball’s height as a function of time during one bounce using both the general and vertex forms of the quadratic equation.

Objectives

  • Record height versus time data for a bouncing ball.
  • Model a single bounce using both the general and vertex forms of the parabola.

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 10 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.

Buy the Book

Go to top

We will be closed on August 21 to allow our employees to enjoy the Great American Eclipse.