## AP Calculus Projects Day 2 – 2015

Here are the projects from Day 1. The projects from Day 2 are below.

Math Behind a Basketball Shot

This group talked about the math behind the ideal basketball shot, including the role Magnus Effect. They recorded some video of them shooting and used the program, Tracker, to analyze position, velocity, and acceleration of the basketball throughout its flight. Here’s a screenshot of the ball at its apex. You can see in the graph that the velocity is zero. (close enough)

Presentation: Basketball Project

Spread of Disease

This student talked about the Ebola scare a few months ago and how Ebola was starting to spread exponentially. He then explained the SIR model and used a hypothetical disease to talk about the infection rates in the town. He checked the formulas by hand and then used a spreadsheet to complete his calculations. The town of 27,830 would be infected by Day 6.

Presentation: Calc project

Parallel Parking

“What is the minimum space needed to parallel park?” This was the guiding question to this students project. She first derived the formula,

and then tested it out in her car. She took the measurements of the car, marked out where she needed to turn and videotaped the result. She only needed one attempt!

Here’s the video.

Presentation: Parallel Parking

Stereographic Projection

This group researched stereographic projection. They were inspired by this model on Thingiverse.

They printed it out and began their investigation. Their original plan was to create their own image but ran into some problems on how to map from the 2D to the 3D. This group worked really hard for the entire time and got into some pretty deep math.

Presentation: Stereographic Projection

Calculus in Economics

This student is going to study Economics in college so this project was right in her wheelhouse. She did a great job of explaining the Demand and Marginal Curves in her presentation. She did some work on the board to support her presentation which I forgot to get a picture of.

Calc Project

Launching a Falcon 9

This group worked on the calculations needed for SpaceX to send the Falcon 9 into orbit. They also got into the math pretty deep and looked for some assistance. Luckily, I attended high school with a current SpaceX employee. I was able to reach out and my students were able to email back and forth with him. He helped them out with some of the calculations and brought their attention to some things they had not thought of. One of the students is going into Aeronautical Engineering so he was very inspired by this project.

Presentation: INTERSTELLAR

Melting Ice Rates

This student compared the melting rates of ice depending on a few variables. One variable was the shape of the block of ice (cylinder, rectangular prism, etc) and the other was tap water vs salt water. She was very diligent and took measurements every 10 minutes for 5 hours!

Still awaiting an email for her presentation which showed all of her calculations and results.

Creating Solids of Revolution

This student took two curves and revolved them around the x-axis. She took these curves and produced the sketches of them in Inventor. She then 3D printed them and calculated their volumes. I will definitely use these in years to come so kids can visualize the solids created by revolutions of curves.

3D Model

Presentation: Solids Of Revolution

Magnetic Acceleration

These students were inspired by videos of railguns they had seen. They created a much smaller, more school friendly version. You can watch the slo-mo video of it here. (The quality is not that great). They calculated that the ball bearings were moving at 8m/s (just under 18mph).

Screenshot of the video

Presentation: The Calculus behind Magnetic Acceleration

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