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
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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):
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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.)
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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
