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w1i - Douglass Houghton Workshop Section 1 Wed Worksheet...

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Douglass Houghton Workshop, Section 1, Wed 10/19/10 Worksheet Indefatigable 1. Suppose you are asked to design the first ascent and drop for a new roller coaster at Cedar Point. (You get to name it, too!) 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 inclines y = L 1 ( x ) and y = L 2 ( x ) with part of a parabola y = f ( x ) = ax 2 + 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 L 1 and L 2 to be tangent to the parabola at the transition points P and Q . To simplify the equations, you decide to put the origin at P . (a) Name your coaster. (b) 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. (c) Solve the equations in (1b) for a , b , and c to find a formula for f ( x ).
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