# 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
1 Identify the values of the constants.
2 Plug the constants into the equation. Simplify the equation.
3 Set the height to zero.
4 Apply the quadratic formula.
5 Since a negative solution does not make sense in this problem, the negative solution is extraneous solution. Discard the extraneous solution.
Example 1
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. https://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.)