Need to find the function to this equation.

Question

Suppose that a 200 feet long suspension bridge has at its end towers that are 100 feet tall. If the cable come with in 15 feet of the road at the center of the bridge, find the function that models the height of the cable above the road a distance of x feet from the center of the bridge.

Answer 1

Suspension bridges are parabolic.  Symmetry about the center allows us to model the shape as y = ax² + c.

 

y(0) = 15. 

 

c = 15.

 

 

 

y(100) = 100.

 

100 = a(100)² + 15

 

a = 0.0085

 

 

y(x) = 0.0085 x² + 15