A suspension bridge with weight uniformly distributed along

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 70 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. (Assume that the road is level.)

Solution

road is suspended from towers whose cables are parabolic in shape, then picture a graph in which 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. Draw a parabola whose vertex is at (0,0), and it curves upward to two points, one on either side of vertex at a distance x= 400 or x= -400, and y for each of these points is 70.

Lets assume parabola whose equation is in the form y = ax^2, that passes through the point (400, 70). Substitute the values of x and y into the given formula and solve for a.

70 = a*(400)^2

a = 70/400^2

So, y = 70x^2/160000

height of the cables at a point 200 meters from the center : y = 70(200)^2/160000

= 17.5 meter