Students will model projectile motion in both function and parametric graphing. This was designed as an in-class modeling activity to be used prior to actually launching air-powered projectile rockets.
A set of data is given in a spreadsheet and students create model functions using a variety of methods: vertex form (then using grab and move to fit the curve to the data points), standard form (using matrices), and quadratic regression.
Before the Activity
This investigation usually follows the study of quadratic functions. The quadratic function is characterized by a parabolic curve, by viewing the scatter plot, we can see it will open downward. The data represents a rocket path, height per unit of time; the symmetry of the curve is obvious. The vertex will represent the height the rocket attained in t seconds. The activity includes parametric graphing, as previously pointed out. The teacher will determine the appropriateness of this activity for classes he/she instructs.
The teacher should review the various forms of a quadratic function and also methods used to create the model function in the different forms. The teacher should also review parametric graphing and any formulas that are necessary for the students to complete this activity successfully.
During the Activity
This activity is designed to be student-centered. The teacher may act as a facilitator while students work independently or cooperatively. The teacher will inform students in which manner they are to work.
The ready-to-use worksheet will provide a written assignment which can be used for daily credit points.
The file titled rocketsimSOL shows the expected results of working through the activity and the screenshots are included in the step-by-step instructions.
After the Activity
Possible Extensions:Students may select quadratic problem examples from internet sites and bring them in and post them for other students to complete for extra credit/ present the problem to the class.
The actual launch of the air-powered projectile can take place outdoors, data collected and returned to the classroom. Students can complete the modeling activities on their collected data.
The marble launcher can be used in the classroom as an alternative method of collecting data.
The air-powered projectile used in the out door activity was purchased from Arbor Scientific.
The actual outdoor launch activity consisted of a vertical launch to determine initial velocity, horizontal launch at different angles, launching at angles with altimeter measurement to create right triangle trigonometry and a probability launch activity.