The Modeling Of The Segment Of A Roller Coaster

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Aim to exploration

The properties of roller coasters can be used in mathematical ways, especially the application and knowledge of differentiation. The roller coaster also can be using functions. This requires careful and particular arranging with safe, even a pleasant experience for riders. This investigation aims to design a rollercoaster comprising of different polynomials - the application and knowledge of calculus processes of derivation and function required in this paper. The first and the second derivative of an equation is used to describe the slop, changes, and the shape of the function. These derivative can be used to discover the point of the function. Algebra is required in this, and it can be displayed of the rollercoaster.

To guarantee that the track is smooth, the lines should change easily. The changes between the direct stretches and the parabola happen at focuses W and Z . For the track to be smooth, the straight stretches of the rollercoaster must ...

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b(0) +C
0=C

the original equation should be :

f(x)=ax^2+ b(x) +C
so f(x)=ax^2+ b(x)

L1 , touching at the point W(0,0). the slope of this function and F(X) is the same ,so what ever the point is the , the first derivative of L1's function is: f(x)=ax^2+ b(x)

f'(x)=2ax+ b

At pint W the slope of the graph is 0.8:


f'(x)=2ax+b

f'(0)=2a(0)+b
f'(0)=0.8
0.8=2x(0)+b
0.8=b

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The original equation should be :
f(X)= ax^2+0.8x


The value f a can be find by using the data of L2 segment. The point of Z is 40 metres horizontally to the right of W(0,0) and the y coordinates of L2 is 40. but we don't know the y value. The second line segment L2is a tangent to ...

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