The Mathematical Association of America (MAA) has a lovely unit on the design of a thrilling roller coaster that uses polynomials and trig to help model certain paths of the roller coaster. This activity is for upper level students who may have had calculus. On the other hand Mathplayground has a nice explanation of what they do when they create the roller coaster. The NCTM has an activity called Roller Coasting Through Functons which looks at the time it takes for a car to complete the fall part. This site discusses all the things the engineer has to consider when designing a roller coaster.
The Futures Channel has a lesson on Roller Coasters including the worksheets to go with it. The link will take you to the pdf file for polynomial roller coasters.
Just found this one which has student use quadratics and linear equations to create a roller coaster. It takes students through a process to create the roller coaster and it looks pretty good.
In addition there are several itunes university and podcasts that provide information on roller coasters including a STEM activity and podcasts by the Michigan Public Radio.
These resources are just a few I found on the internet and could be used either has a unit within math or as an exercise to show a real world application of polynomials.