### Activity

## Classroom Idea: Quadratic Rocket Physics

### Subject

Mathematics (NYS P-12 Common Core)

### Grade Levels

Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

### Note

This "classroom idea" is provided to illustrate examples of each performance indicator. Teachers should feel free to use it or adapt it if they so desire. Some of the ideas exemplify more than one performance indicator and/or incorporate topics in science and technology. In those instances, the appropriate performance indicators will be identified.

### Authors

Mathematics Resource Guide with Core Curriculum Writing Team

### Description

Physicists tell us that the altitude h in feet of a projectile *t* seconds after firing is *h = -16t ^{2} + v_{u}t + h_{o}* where

*v*is the upward component of its initial velocity in feet per second and

_{u}*h*is the altitude in feet from which it is fired. A rocket is launched from a hilltop 2400 feet above the desert with an initial upward velocity of 400 feet per second. When will it land on the desert? Discuss what the discriminant can tell you about the solution to this problem. Then use the quadratic equation to find the solution and explain your answer.

_{o}### Source

Mathematics Resource Guide with Core Curriculum Writing Team. "Classroom Ideas." *Mathematics Resource Guide with Core Curriculum,* New York State Department of Education, 152.