## 5.1 Case Study: Sleuthing Galileo

### Summary

Galileo conducted rolling ball experiments in which he put a ramp with a horizontal ledge at the bottom on a table. Then he rolled a ball down the ramp recording how far out it hit the floor for a given starting height. The purpose of this CSC is to use calculus and modern analysis to try to make mathematical sense of the five data points that he recorded in this experiment. One outcome of the investigation is to formulate some ideas about how this particular experiment might have contributed to a calculation of g, the acceleration due to gravity.

By the time you complete the CSC, you should know:

• How to work with one or more classmates on a team project. (This is not necessary but is encouraged.)
• How to write a CSC report, especially the Interpretation and Summary.
• This CSC as another example of applying mathematics you have learned to solving a real-world problem, this time a detective puzzle.

### Applets

Sleuthing Galileo

### Videos

See short videos of worked problems for this section.

### Exercises

See Exercises for 5.1 Case Study: Sleuthing Galileo (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

#### Interesting Application

Galileo's own notes on the rolling ball experiment.

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel