Stanton D. answered • 07/27/20

Tutor to Pique Your Sciences Interest

Hi Nyugen N.,

So sketch what you think might be an "exciting" roller coaster course. Then go back into your "grab bag" of possible functions, to select types that might provide that.

I suggest that roller coaster rides are more exciting fast, so boost your ride up to the 75 m initially, then "let it go" from there. sin, cos, rational functions (of x^-values) and polynomials provide vertical wiggles; the other functions are useful for matching the slopes between segments, perhaps (that prevents physical destruction of the car and the track!).

How do you match slopes between segments? You could combine functions as "wedges", e.g.: x/200*sin(x) + (200-x)/200*exp(-x^2) would combine an increasing "wedge" of sine function with a decreasing "wedge" of exp(-x^2) function, for example. (But that doesn't meet the design criteria, it's just for an example of type). You can see that this summed function would have the slope of the exp(-x^2) at x=0, and the slope of the sin(x) at x=200. If you then do a following "wedge" with sin(x) and some other function, in the same way, that would automatically have a non-jolting transition at x=200, since the total function would be just sin(x) at that point.

-- Cheers

-- Cheers, -- Mr. d.