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 coordinate system at the vertex.
[Note: This equation is used to find the length of cable needed in the construction of the bridge.]
The equation of parabolic section of the bridge is shown in figure (1).
A suspension bridge with its cable is parabolic shape is as shown in figure (1).
Distance between the two towers of the bridge is and the lowest point of the cables from the top of towers is .
The general equation of a parabola with vertical axis where vertex and focus at is given by,
Where is the directrix.
1) If , then parabola opens downward.
2)If , then parabola opens upward.
Width of a parabola is given by .
Height of a parabola is given by .
Since, given parabola is drawn with vertical axis, the general equation will be given as,
As the parabola opens upward,
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started