A suspension bridge with weight uniformly distributed along its length has twin towers that extend 85 meters above the road surface and are 800 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 200 meters from the center.

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 85 meters above the road surface and are 800 meters apart.

Let the road surface is the x-axis, and the point (0,0) represents the point that is on the road surface midway between the two towers.

Now it will form an upward parabola whose vertex is at (0,0), one on either side of vertex at a distance x= 400 or x= -400, and y for each of these points is 85.

The equation of parabola is: [tex]y=ax^2[/tex]

Substitute (400,85) in above formula

[tex]85=a(400)^2[/tex]

[tex]\frac{85}{160000}=a[/tex]

Therefore, the required equation is [tex]y=\frac{85}{160000}x^2[/tex]

We need to Find the height of the cables at a point 200 meters from the center.

So substitute x=200 in above equation.

[tex]y=\frac{85}{160000}(200)^2[/tex]

[tex]y=\frac{85}{160000}(40000)[/tex]

[tex]y=\frac{85}{4}[/tex]

[tex]y=21.25[/tex]

Hence, the required height of the cable is 21.25 meter