# Projectile Motion

Author: Anne Gloag    ### Project Details

The students design and construct a repeatable and quantifiable demonstration of projectile motion using low cost materials (PVC pipe, plywood, rubber bands, etc). They brainstorm and design a device. They construct their device and execute several tests. Students need to use your knowledge of quadratic functions in order to hit a target. They also need to collect and analyze data in order to determine how the motion of your projectile depends of factors such as angle of elevation and initial velocity.

What Went Well With This Project:

The students really liked the hands-on aspect of the project. They connected the equations and mathematical methods they learned in the direct instruction component of the unit with a concrete application. I found that when I come back and talked about functions in the classroom I could refer back to this project in order to get students to think what x-intercepts mean and what the maximum and minumum points of a function mean.

What I Would Do Differently Next Time:

I think that the project was hard to manage because I required student to bring in their own materials. Some groups were very organized and brought all their materials on the due date thus they started working on building their device straight away. However, some groups took almost a week to bring their materials to school and as a result they had nothing to do and fell behind the other students. Next time I do this project I need to allow a week between the design stage and the construction stage so that everyone can start building at once. The other option would be for me to bring in all the necessary materials. The problem with the second option is that I think that it might stiffle creativity.

Recommendations For Others Who Want To Try This Project:

The data collected from this project is not very accurate. There are many factors that causes this. Some of them are physical factors: air resistance, wind, getting the projectile airtight but I think that these factors are valuable to discuss in class. Other factors are related to the accuracy of building, launching and measuring. These factors are totally dependent on the students involvement in the project and willingness to improve, adjust and repeat. It takes a lot of patience on the part of the teacher to constantly encourage students to improve their work. I think that this teaches students a good work ethic and it is worth that time and I noticed that the students start to self-correct and evaluate their own work with a critical eye.

• Design Proposal
• Competed Ballistic Device
• Initial Testing Report
• Redesign Report
• Angles of Elevation Data Analysis
• Presentation
• Reflections

What Will Students Be Able To Do:

1.      Use two-dimensional equations of motion for projectile motion to calculate initial velocity, time in the air, horizontal distance and maximum height.
2.      Use trigonometry to resolve two-dimensional vectors into its vertical and horizontal components
3.      Graph quadratic equation and find x-intercepts, y-intercepts and vertex
4.      Apply factoring, quadratic formula and graphing calculator to find x-intercepts of a quadratic graph

Algebra II standards
8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

Trigonometry standards
12.0 Students use trigonometry to determine unknown sides or angles in right triangles.
19.0 Students are adept at using trigonometry in a variety of applications and word problems.

Physics standards
1i. * Students know how to solve two-dimensional trajectory problems.
1j. * Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.

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