# Parabolas in Flight

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 Keywords: algebra quadratics trajectory Subject(s): Physics, Math, Algebra, Calculus, Technology, Video Grades 9 through 12 School: Hartford High School, White Riv Jct, VT Planned By: Nancy Kent Original Author: Nancy Kent, White Riv Jct
Unit of Study - Quadratic Equations
Essential Question - "Can you generate the mathematical model to calculate the flight of a football?"
ISTE Standards:
1. Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:
a. apply existing knowledge to generate new ideas, products, or processes.
b. create original works as a means of personal or group expression.
c. use models and simulations to explore complex systems and issues.

Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students:
a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media.
b. communicate information and ideas effectively to multiple audiences using a variety of media and formats.

Lesson:
In groups of 3, students will FLIP video a trajectory. It may be a football pass, basketball shot, soccer kick or any other ball they would like to use. The students will import their video into Windows Movie Maker and use the timer to find the total time of the flight. Using the trajectory formula: H(t) = -1/2gt^2 + vot + ho, the students will use the gravity constant to find the “a” value of the quadratic equation and an estimate of the release height for the “c” or constant value of the equation. Then using half the flight time, as the vertex of the parabola, they will find the” b” term using the vertex formula = -b/2a. After completing the formula, the students will make a t-chart of the height of the ball during flight. They will verify the height using an object in the background. (examples of this year's videos below)

I have expanded the unit for Calculus by having them find the first derivatives to make a chart of velocities. If they have parent permission, they will upload to teachertube.com to share with a global audience. (examples of this year's videos below)