The Calculus behind Roller Coasters

# The Calculus behind Roller Coasters - Rock Sims Calculus...

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Rock Sims 3/20/08 Calculus 141 The Calculus behind Roller Coasters This project was designed for us to use 5 given equations to make a system of 16 equations with unknown values to construct a roller coaster that is continuous and smooth throughout. The project required us to use Maple to define piecewise functions and define a system of equations. The project also requires knowledge about derivatives so the roller coaster has a smooth curvature the entire way through and the car does not change speed too drastically. The rest of this paper will elaborate on the problems used and include examples of many of them. The project worksheet gives us 5 equations… F1(x) =2.5x This equations represent the initial ascent of the roller coaster to it’s highest point. This straight line makes up the first 20 feet of the track and the slope is 2.5. -- F2(x) =a(x^3)+b(x^2)=cx+d F3(x) =e(x^3)+f(x^2)+gx+h F4(x) =i(x^3)+j(x^2)+kx+l The above 3 equations are 3 cubics which will form the ascensions and descensions that make up the next 300 feet of track and the track must reach a height of

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The Calculus behind Roller Coasters - Rock Sims Calculus...

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