SOLUTION: Bridge design: A cable of a suspension bridge is suspended (in the shape of parabola) between two towers that are 120 meters apart and 20 meters above the roadway. The cable touche

Question 912916: Bridge design: A cable of a suspension bridge is suspended (in the shape of parabola) between two towers that are 120 meters apart and 20 meters above the roadway. The cable touches the roadway midway between the towers.
a) Find an equation for the parabolic shape of the cable.
b) Find the length of the parabolic cable.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A cable of a suspension bridge is suspended (in the shape of parabola) between two towers that are 120 meters apart and 20 meters above the roadway. The cable touches the roadway midway between the towers.
a) Find an equation for the parabolic shape of the cable.
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You have 3 points and want to find a parabola that passes thru them
Make the points (-60,0), (0,-20) and (60,0)
-60 and 60 are solutions of the equation of the parabola, and -20 is the vertex.
---
y = k(x-60)*(x+60) = k*(x^2 - 3600)
To make the vertex -20, k = 1/180
--> y = (x^2 - 3600)/180
That's "an equation." You can add 20 to make the road at y = 0
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b) Find the length of the parabolic cable.
It's symmetrical about the y-axis, so find 1/2 the length from x = 0 to x = 60.
L/2 = INT
dy/dx = x/90
L/2 = INT
L/2 = (1/90)*INT
L/2 =
@ x = 0 -->
@ x = 60 -->
@ x = 60 -->
=~ 266.6784
--------------------
@ x = 0 -->
=~ 202.4914
--> L/2 =~ 64.187
L = 128.374
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A hanging cable is not a parabola. It's not that simple.
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