Illustrate the problem and show your complete solution.

Question

The cable of a suspension bridge hangs in a parabolic arc form with the weight spread evenly along it. Given the following conditions, find the distance from the roadbed to the cable at the points on the roadbed found at 50-foot intervals from the center: i. The bridge is 300 feet long. ii. The towers are 60 feet high. iii. The cable is 20 feet above the roadbed at the center.

Answer 1

Put the vertex of the parabola at the point (0,20).

 

Then, an equation of the parabola is y = a(x-0)² + 20

 

Since the points (±150, 60) lie on the graph, we have:

 

     60 = a(150)² + 20

 

             a = 40/62500 = 2/3125

 

So, when x = 50, y = (2/3125)(50)² + 20 = 21.6 feet