1) Research a favourite, or a famous, rollercoaster. Write a short summary (2-3 paragraphs) of this coaster’s general information; include its name, a picture, where it is located, when it was built, why you picked it and its physical characteristics.
Make sure you note the height of the initial drop as the initial drop of the rollercoaster you will be designing in this assignment will model the initial drop of this rollercoaster you have researched. Also remember to cite your sources (1-2 sources).
2) It may be useful now to do a little bit of research on the physics of rollercoasters. You will not need to do any physics-style calculations in this assignment, but you will be expected to abide by the common rules. For example; a rollercoaster cannot be expected to defy gravity, it must be given momentum at the beginning of the track, and cannot reach as high a height at the end of its track as it can at the beginning. Write a short paragraph describing what you found and cite your sources (1-2 sources) .
3) Now it is time to create your own rollercoaster. Using the idea of piecewise functions, create an appropriate scale on your axes and design a rollercoaster, using technology like Graph. You rollercoaster must have the features listed below. If you are unsure about piecewise functions, or how to express them, this is a good time to do some independent research on their proper use and notation.
You should try to make each of the polynomial functions flow into one another to create a smooth ride for your passengers. To prevent your functions from overlapping, make sure to restrict the domain of the function. Set each polynomial function to a different colour and submit a picture (or a screen capture) of your design, as well as the piecewise function notation that models it.
a) Uses at least four different polynomial functions, pieced together.
b) Models the initial drop of the rollercoaster you researched.
c) Has at least 4 other drops.
d) Goes through an underground tunnel at least once (assuming y = 0 is the ground)
c) Any other features you feel would add to the ride and can be modelled with a polynomial function.
4) For each of the pieces in your design:
a) State the equation for the polynomial function used.
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