New Jersey Six Flags, Nitro Roller Coaster
This is my real life parabola, this is Nitro located in Six Flags in New Jersey. All roller coasters are based on parabolas. They use parabolas to measure the steepness of the drops, so the coaster can function well.
Why is the picture sideways? Also, not sure about what you mean by measuring steepness. Please supply details. My suggestion would be that you use picture of a roller coaster from the side as it comes down and then goes back up. You may get something close to a sine wave.
As I showed you in class, you can think of a sine wave as composed of alternating pieces of up-parabolas and down-parabolas. It would be interesting to see how closely a sine graph comes to this construction. See the followign diagram for an example of what I am envisioning:
http://www.cabrillo.edu/~jmccullough/Example_Problems/Conservation_Energy_P2.JPG