The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 600feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point of 150 feet from the center of the bridge?

Corinne Woods

Corinne Woods

Open question

2022-08-31

The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 600feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point of 150 feet from the center of the bridge?

Answer & Explanation

Arturo Mays

Arturo Mays

Beginner2022-09-01Added 12 answers

Use the form of the parabola:
y = a ( x k ) 2 + h
where k is horizontal shift, h is vertical shift and a is verticalstretch/inversion factor
Call midway between the towers 0, so the bridge touches the road at(0,0). Thus the formula for the parabola is y = a x 2
Then plug in some numbers:
you know at x = 300 (from center to supporting cable), y =80. Plug this into the above equation to get the formula forthe parabola:
y = .000889 x 2
Therefore, at x = 150, plugging into the above equation, y = 20 ft high

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