Parabolic Bridge question need help?
a parabolic bridge is 40m wide. Determine the height of the bridge 12m in from the outside edge, if the height 5m in from the edge is 8m
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This is no easy problem.
see http://ceprofs.tamu.edu/rbruner/vertical/sld008.ht...
The general equation is y(x) = a x^2 + g1 x + c, let c = 0 (initial elevation)
a is a function of grade in, g1, grade out, g2 (which is negative) and the length of the curve.
Since grade in is positive and equals grade out we can solve for a in terms of g1, since a = r/2 and since r = (g2 - g1)/L = - 2 g1/L. Since L = 40, the r = - g1/20. Hence a = - g1/40
Substituting then we get Y (x) = - g1/40 x^2 + g1 x for our formula.
Follows that 8 = - g1/40 * 5^2 + g1 * 5, and solving for g1 we get:
g1 = 1.828 and a = -g1/40 = -0.0457 for our constants.
Finally, for Y (12) = 15.35 m TA DA lol