Free Fall according to Galileo

The purpose of this page is to help you understand 1 dimensional accelerated motion and develop related skills. Be prepared to answer or do all the following:

**Section 1: Development of the theory:**

- Compare the method Galileo used to convince his readers with other styles of writing. [Hint: Most books of Galileo's day were written in the style of Euclid's
**Geometry**.] - Galileo defined acceleration as....
- A football is kicked straight upwards. Compare its ACCELERATION
*[both magnitude AND direction]*- just after being kicked, while it is going up,
- at the instant it reaches its greatest height, and
- while coming down, just before it is caught.

- Derive Galileo's famous equation, d = 1/2 at
^{2}from basic equations and assumptions. - What are the limiting conditions on Galileo's equation: d = 1/2 at
^{2}? - No team obtained results from Galileo's Lab (Experiment I-2: Free Fall) in perfect agreement with Galileo's equation. Discuss if this
Galileo wrong. Explain.*proves* - What were Galileo’s beliefs on motion? How were they different from Aristitle’s? What did Galileo do to convince himself that his ideas were correct?
- Why did Galileo NOT directly test his theory of falling objects?
- In what time period did Galileo live?
- What is the numerical value of the acceleration of a falling object near the surface of the earth?
- What is Galileo's
*principle of relativity?*

**Section 2: Mathematical section: Apply your understanding by making specific predictions.** List all equations you use, and show substitutions and algebra. Show your stepwise solution procedure. Answers need to be reported with the correct *uncertainty* (*i.e., the correct number of significant figures*), and appropriate unit labels:

- A ballast sand bag is dropped from a hot air balloon. Ignoring friction as insignificant, and presuming the balloon is high enough so the bag has not hit the ground, how
**fast**would you expect the bag to be travelling 5.0 seconds after release? - What will be the bag's
**average speed**for the first 5.0 seconds after release? - What
**distance**will the bag transverse in those 5.0 seconds after release? - A gun is fired STRAIGHT UPWARDS with an initial bullet speed of 100 m/sec. How
**long**will it take for the bullet to reach its highest position and stop rising? - What will be the
**maximum altitude**attained by the bullet? - Presuming friction is insignificant, what will be the bullet's
**speed**5.0 seconds after fired? - How
**long a time**will it take the bullet to rise and return to the ground?

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created 16 September 2001

last revised 15 May 2010 by D Trapp

or to site menu

created 16 September 2001

last revised 15 May 2010 by D Trapp