Concept explainers
Suspension Bridge In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 600 m apart, and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the
To find: The equation of the parabolic part of the cables, by placing origin of the coordinate system as the vertex. Use it and find the length of the cable used in the construction of suspension bridge.
Answer to Problem 55E
The equation of the parabolic part of the cables is
Explanation of Solution
Given:
The distance between the tower is
Definition used:
“The equation of the parabola with vertex
Formulae used:
“The length of the curve
Calculation:
Let the equation of the parabolic part of the cable be
Now assume the vertex of the parabolic part of the cable be origin.
That is,
The distance between the tower is
The axis (y-axis) divides the span in to two equal halves.
Therefore, the point
Now AB the diameter passing through the point
Therefore, the end points of the diameter AB are
Since, the points
Substitute
Substitute
Therefore, the equation of the parabolic part of the cable is
Find the length of the cable used in the construction of suspension bridge as follows.
Rewrite the equation as
In this problem for the parabolic part the string is used between the lines
By evaluating the integral obtain the length of the string used in the construction of the suspension bridge.
Therefore, the required equation of parabolic part of the cable is
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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