An experimental model for a suspension bridge is built In on

An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching there, and up again to the top of a second tower. The towers stand 80 inches apart. At a point between towers and 24 inches along the road from the base of one tower, the cable is 2.56 inches above the roadways. Find the height of the towers.

Solution

THe shape of the cable would be parabola:

Lets assume the the point where cable touches the road is on origin of the coordinate axis at point ( 0, 0)

It extends both side of x axis from ( -40 to 40)

Now, one point on the parabola which is 24 inches from 1 tower and ht. 2.56 inches : (-16 , 2.56)

So, equation of parabola : y = a(x-h)^2 +k

(h , k) = (0. 0)

So, y = ax^2

2.56 =a(16)^2 ---> a= 2.56/256 = 0.01

Equation of parabola: y = 0.01x^2

Now to find height or y coordinate at the point at which x = +/- 40

So, y = 0.01(40)^2 = 16 ft is the height of towers