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That’s the Way the Ball Bounces – Height and Time for a Bouncing Ball

Experiment #10 from Real-World Math with Vernier

Education Level
High School


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.


  • 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 features the following sensors and equipment. Additional equipment may be required.

Option 2


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This experiment is #10 of Real-World Math with Vernier. The experiment in the book includes student instructions as well as instructor information for set up, helpful hints, and sample graphs and data.

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