Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Quadratics

9-12

50 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

• ##### Accessories

CBR™/CBR 2™
Sensor - Microphone

## Sound of the Bouncing Ball

#### Activity Overview

In this activity, students will develop a mathematical model that is based on the time interval of the sound the ball makes on impact between consecutive bounces. They will then use the model to predict how long the ball would (theoretically) bounce.

#### Objectives

• Analyze the time intervals between consecutive bounces of a ball;
• Determine the decrease in the length of the time interval between bounces;
• Compare the time intervals to rebound height measured with CBR 2™;
• Determine the relationship between time intervals and rebound height;
• Develop a mathematical model for the decreasing time intervals.

#### About the Lesson

Most students instinctively know already that for each consecutive bounce, a ball will reach slightly less height than in the bounce before. Maybe they even have explored the mathematical model that describes how the height is decreasing for a series of bounces. In physics classes, they might have explored the relationship between conservation of mechanical energy in the constant exchange between potential and kinetic energies and the diminishing rebound height.

Students will explore that relationship from a slightly different perspective. Can we develop a mathematical model that is based on the time interval of the sound the ball makes on impact between consecutive bounces? And can we then use our model to predict how long our ball would (theoretically) bounce?