The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

We realize that the vertex is at the absolute bottom of the link. The beginning of the facilitate plane is taken as the vertex of the parabola, while its upward hub is brought the positive

   

Diagrammatic portrayal is as per the following:

Here,

   

are the longest and the most brief wires, separately, appended to the link.

DF is the supporting wire appended to the streets,

   

from the center.

Along these lines,

   

The condition of the parabola is of the from

   

(as it is opening upwards).

The directions of point A are

   

Since,

   

is a point on the parabola.

   

Condition of the parabola,

   

The

   

of point

   

Henceforth, at

   

   

Hence, the length of the supporting wire attached to the roadway 

   

from the middle is approximately