That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
Recommended for grades 9–12.
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
where y represents the ball’s height at any given time x. Another form of a quadratic equation is
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 experiment requires each of the following Vernier sensors and equipment (unless otherwise noted):
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 Made Easy »
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.