Results 1 to 1 of 1

Thread: Building a better roller coaster

  1. #1
    Mar 2010

    Building a better roller coaster

    Calculus.. Building a better roller coaster?

    Suppose you are asked to design the first ascent and drop for a new roller coaster. By studying photographs of your favorite coasters, you decide to make the slope of the ascent 0.8 and the slope of the drop -1.6. You decide to connect these two straight streches y = L1(x) and y = L2(x) with part of a parabola y = f(x) = ax2 + bx + c, where x and f(x) are measured in feet. For the track to be smooth there can't be abrupt changes in direction, so you want the linear segments L1 and L2 to be tangent to the parabola at the transition points P (from L1 to the parabola) and Q (from the parabola to L2). To simplify the equations you decide to place the origin at P.

    1-a) Suppose the horizontal distance between P and Q is 100 feet. Write equations in a, b, and c that will ensure that the track is smooth at the transition points.

    1-b) Solve the equations in part (a) for a, b, and c to find a formula for f(x).

    1-c) Find the difference in elevation between P and Q.

    The solution in Problem 1 might look smooth, but it might not feel smooth because the piecewise defined function (consisting of L1(x) for x < 0, f(x) for 0 < x < 100, and L2(x) for x > 100) doesn't have a continuous second derivative. So you decide to improve the design by using a quadratic function q(x) = ax2 + bx + c only on the interval 10 < x < 90 and connecting it to the linear functions by means of two cubic functions:

    g(x) = kx3 + lx2 + mx + n for 0 < x < 10

    h(x) = px3 + qx2 + rx + s for 90 < x < 100

    2-a) Write a system of equations in 11 unknowns that ensure that the functions and their first two derivatives agree at the transition points.

    2-b) Solve the equations in part (a) with a computer algebra system to find formulas for q(x), g(x), and h(x).

    Particularly help with PART 2 Please....
    Last edited by GiorgioCabrera; Mar 22nd 2010 at 10:43 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Help on roller coaster sine function
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Jan 19th 2011, 06:58 PM
  2. Roller Coaster Dynamics
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: Jun 9th 2009, 05:03 PM
  3. Roller Coaster Max Altitude
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Nov 28th 2008, 06:08 AM
  4. Roller coaster
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Jul 9th 2007, 11:15 AM
  5. The garden roller problem (trigonometry)
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Aug 17th 2005, 06:31 PM

Search tags for this page

Click on a term to search for related topics.

Search Tags

/mathhelpforum @mathhelpforum