Students will explore the use of parametric equations to model the motion of the 'Human Cannonball' after being fired from a cannon. Key graph features will be explored, including maximum height, length of time in the air, and maximum distance traveled through the use of parametric equations and a quadratic regression equation. The quadratic equation will be determined by grabbing points from the graph of the parametric equations.
Before the Activity
Prior to this activity, students should receive some preliminary training in parametrics. In particular, they should have an understanding of the 3 variables involved (x, y, t) and the vertical and horizontal components of motion. The attached .tns files should be loaded and the humancannont.doc file should be reviewed by the instructor.
During the Activity
The student guide should be provided to students. The questions at the end are optional. The instructor may choose to collect the completed .tns files from students for review at the end of this activity and eliminate the questions page.
After the Activity
Several problems are provided along with a key to further the study of parametric equations. Some of these problems involve additional challenges, such as determining if a ball will make it over a fence.