Question

An engineer designs a cable of a suspension bridge that hangs in the form of a parabola, the
towers supporting the cable are 360 meters apart. The cable passes over the supporting towers at a height of 80 meters above the roadway and the lowest point of the cable is 10 meters above the roadway Find the lengths of the vertical supporting rods from the cable to the roadway at intervals 60 meters from the center of the bridge to a supporting tower?

Answer 1

Set up the parabola with its vertex at (0,10). The equation is
y = ax^2 + 10
Since the 80m towers are 180 meters from the center,
a*180^2 + 10 = 80, so a = 7/3240
Thus the equation is
y = 7/3240 x^2 + 10
Now just find y at x = ± 60,120