SOLUTION: The cable of a horizontal suspension bridge are supported by two towers 120 feet apart and 40 feet high. if the cable is 10 feet above the floor of the bridge at the center. how hi
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Question 1199364: The cable of a horizontal suspension bridge are supported by two towers 120 feet apart and 40 feet high. if the cable is 10 feet above the floor of the bridge at the center. how high is the cable 10 feet from the end of the bridge? Found 2 solutions by Alan3354, ikleyn:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The cable of a horizontal suspension bridge are supported by two towers 120 feet apart and 40 feet high. if the cable is 10 feet above the floor of the bridge at the center. how high is the cable 10 feet from the end of the bridge?
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It's not specified, but it's usually assumed that the cables are in the shape of a parabola. It's actually a catenary under its own weight, but the load of the bridge makes the distinction irrelevant.
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Assuming it's a parabola:
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Put the Origin at the center of the cable (above the center of the bridge). Use the 3 points, (-60,30), (0,0) and (60,30) to find the equation.
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Can you do the rest?
You can put this solution on YOUR website! .
The cable of a horizontal suspension bridge are supported by two towers 120 feet apart and 40 feet high.
If the cable is 10 feet above the floor of the bridge at the center, how high is the cable 10 feet from the end of the bridge?
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If we place the origin of the coordinate system at the bridge level midpoint between the two towers,
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. It is the only unknown in this problem now.
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 = .
Having this equation ready, we substitute x = 50 ft into the equation
and find the height of the cable at the point x= 50, which is 10 feet from the end of the bridge
y = = 30.833 ft (rounded). ANSWER
