Interactive Lecture Demonstration 2 – Basketball Bounce

In this activity, a basketball will be held directly underneath a Sonic Ranger and then dropped onto the floor. The Sonic Ranger will create a position versus time graph for the basketball.

1. What mathematical shape does the position vs. time graph for a freely-falling object have ?

2. Sketch your predicted position vs. time graph for the basketball (assume that the ball will bounce at least 3-4 times). Remember which direction the Sonic Ranger defines to be positive ! Label clearly on your graph the position of the floor. Numbers are not necessary on your axes, but labels are.

3. We will now do a quadratic regression analysis of one of the ball's bounces (i.e. for the period of time between two successive contacts of ball with floor). Write the mathematical equation that describes a quadratic function. Directly below your math equation, write the physics equation that describes the position vs. time graph for the bounce. Then match the variables in the two equations by drawing a circle around each combination of corresponding math and physics variables.

4. Write the actual regression equation (including correct units on the fit parameters) below.

5. Now use your matched math and physics variables, and the results of the regression analysis, to determine the acceleration of the ball during its bounce. Show your calculation completely.

6. How does your result compare with the value that you expect ? List at least two factors that could explain a difference between the expected value and the value you found.