help with word promblem need answer

Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend 75 meters above the road surface and are 400 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 100 meters from the center. (Assume that the road is level.)

Answer 1

This describes a parabola with vertex at the middle of the bridge, concave up.  Place the origin at the middle of the bridge.  The equation of this parabola is

 

y = ax²

 

At opposite ends, x = ±400/2 = ±200, and y = 75

 

75 = a(200)² = a(-200)²

 

a = 75 / 200² = 1.875 x 10^-3

 

Then

 

y = (1.875 x 10^-3)x²

 

At x = 100,

 

y = (1.875 x 10^-3)(100²) = 18.75

 

The cable height is 18.75 m above the bridge at 100 m from the center of the bridge.