Site: US and Canada

Bouncing Ball

Published on 10/17/2008

Activity Overview

In this experiment, students collect the height versus time data of a bouncing ball using the CBR 2™. This activity investigates the values of height, time, and the coefficient A in the quadratic equation, Y = A(X - H)2 + K, which describes the behavior of a bouncing ball. They graph scatter plots, graph and interpret a quadratic function, apply the vertex form of a quadratic equation, and calculate the maximum value of a parabola.

Before the Activity

  • Use TI Connect™ to download Vernier EasyData™ application
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 105 - 116 from the attached PDF file for the class

  • Set up the calculator and CBR 2™ for data collection
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Drop a ball from a position 15 centimeters below a CBR 2 and collect data of it bouncing
  • Plot the distance versus time data
  • Analyze the data in one of three ways

  • A. Analyze data from within App:
  • Select region to be analyzed (parabola)
  • Find the regression equation for the quadratic fit

  • B. Exit the App and let calculator identify a regression equation:
  • Plot the time versus distance data on the calculator
  • Select a region and identify the data points from the region and store as lists
  • Plot the data points (parabola) and find a regression equation for it

  • C. Observing vertex form of parabola and it relationship with a quadratic equation:
  • Use parabola plotted earlier with stored coordinates
  • Store the coordinates from the vertex in the standard variables
  • Enter equation A( X - H )2 + K, graph the equation, and explore different values of A
  • Find value of A that best fits the parabola
  • Since the ball is dropped, the value of A is negative and is found to be one-half the acceleration due to gravity
  • After the Activity

  • Students analyze the results and answer the case analysis questions on the student worksheet.
  • Review student results
  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary