# Activities

• • • ##### Subject Area

• Math: Algebra II: Data Analysis
• Math: Algebra II: Logarithms and Exponentials
• Math: Algebra II: Transformations

• ##### Author 9-12
College

60 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

CBR™/CBR 2™

• ##### Other Materials
Large bouncy ball (at least 20 cm in diameter).
2 meter sticks.
Clamp to attach CBR2 to a ceiling fixture.

## Determining the Bounciness of a Ball using a CBR2 and TI-Nspire

#### Activity Overview

The objective in this lab is to find a functional relation between bounce height and number of bounces of a ball dropped from a certain height above the ground (i.e. the height of each subsequent bounce, after the ball is released, plotted against the bounce number) and to use this function to determine the bounciness (or "bounce-coefficient") for the ball.

#### Before the Activity

A suitable location in a hallway or classroom with a hard floor needs to be found. The CBR2 needs to be clamped to some kind of ceiling fixture (e.g. an Exit sign or dropped ceiling framework) so that it is at least 2 meters above a hard, smooth, flat floor.

Test the suitability of the location by dropping the ball from a height of approximately half a meter BELOW the CBR2. The ball should be able to continue bouncing under the CBR2 for at least 5 bounces without straying too far from the drop point (i.e. staying within a circle of no more than 1 meter diameter).

#### During the Activity

Students should work in teams of 3 or 4 to carry out this experiment. The detailed instructions for collecting the data are provided in the attached file. The data collected by the CBR2 motion detector are distance versus time data (distance of the bouncing ball from the detector versus time elapsed since the ball was dropped).

#### After the Activity

Following data collection, the students are directed to transform the data so as to generate a graph of inverted parabolas that depicts the series of bounces with decreasing heights. Using this transformed graph, students generate a new set of derived data for the height of each subsequent bounce and plot bounce-height against bounce-number (rather than elapsed time). They create a scatter-plot of these derived data (bounce-height versus bounce-number) and then attempt to find a function to fit these data points. Using their fitted function, students can estimate the "bounce-coefficient" of the ball and the eventual height at which the ball comes to rest (which should approximate the diameter of the ball).