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

Recommended for High School.

## 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 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* »