SOLUTION: The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high. If the cable is 10 ft. above the floor of the bridge at the center, find t

Algebra.Com
Question 1190859: The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high. If the cable is 10 ft. above the floor of the bridge at the center, find the equation of the parabola using midpoint of the bridge as the origin. (Note: A suspension bridge cable hangs in a parabolic arc if the weight is distributed uniformly along the horizontal.)
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart and 40 ft. high.
If the cable is 10 ft. above the floor of the bridge at the center, find the equation of the parabola
using midpoint of the bridge as the origin.
(Note: A suspension bridge cable hangs in a parabolic arc if the weight is distributed uniformly
along the horizontal.)
~~~~~~~~~~~~~~~~~

If we place the origin of the coordinate system at the bridge length midpoint, we have the vertex of the parabola
at the point (0,10).


So, we write an equation of the parabola in vertex form

    y = ax^2 + 10.


Coefficient "a" is unknown.  To find it, we use the condition at the endpoint: y= 40 at x= 120/2 = 60.
It gives

    40 = a*60^2 + 10

    40 - 10 = a*3600

       30   = 3600a

        a   =  = .


Thus the parabola is  y = .      ANSWER

Solved.



RELATED QUESTIONS

The cables of the horizontal suspension bridge are supported by two towers 120 ft. apart... (answered by ikleyn)
The cables of a horizontal suspension bridge are supported from two towers 40 ft high and (answered by ankor@dixie-net.com)
The cables of a horizontal suspension bridge are supported by two towers 120 feet apart... (answered by Alan3354)
The cable of a horizontal suspension bridge are supported by two towers 120 feet apart... (answered by Alan3354,ikleyn)
The cables of a horizontal suspension bridge are supported by two toers 120 m apart and... (answered by solver91311)
The cables of a horizontal suspension bridge are supported from two towers 40 feet high... (answered by solver91311)
The cabels of a suspension bridge are in the shape of a parabola. The towers supporting... (answered by solver91311)
The cable of suspension bridge hangs in the shape of a parabola. The towers supporting... (answered by ikleyn)
A cable of a suspension bridge is suspended (in the shape of the parabola) between the... (answered by Alan3354)