# Projectile Motion

Pronunciation: /prəˈdʒɛk.taɪl ˈmoʊ.ʃən/ Explain

Projectile motion is the vertical motion of an object in a gravitational field given an initial velocity and height. The quadratic equation for projectile motion is:
where t represents time, a represents acceleration due to gravity, v0 represents the initial velocity, and h0 represents initial height. Since down is taken to be negative, acceleration due to gravity is a negative number.

### Manipulative

 Click on the blue points on the sliders and drag to change the figure. What initial angle would make the projectile go only up or down? Manipulative 1 - Projectile Motion Created with GeoGebra.

### Example

1. Jeff is standing on top of 20 foot tower. He throws a stick down at an initial velocity of -10 ft/s. Use -32 ft/s2 for the acceleration due to gravity. What is the equation for the vertical height of the stick? At what time does the stick reach the ground?

StepEquation(s)Description
1Identify the values of the constants.
2Plug the constants into the equation. Simplify the equation.
3Set the height to zero.
5Since a negative solution does not make sense in this problem, the negative solution is extraneous solution. Discard the extraneous solution.
Example 1

### References

1. McAdams, David E.. All Math Words Dictionary, projectile motion. 2nd Classroom edition 20150108-4799968. pg 145. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Projectile Motion. 4/28/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/projectilemotion.html.

### Revision History

4/28/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)