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Math Help - Help finding equations for parabolas

  1. #1
    Rae
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    Help finding equations for parabolas

    The shape of a flexible and inelastic cable supporting a load that is uniformly distributed horizontally, like the cables of a suspension bridge, is a parabola.

    a) Place the origin of an xy-coordinate system at the lowest point of a parabolic cable of a suspension bridge whose span is "L" and sag is "h." Find an equation for the cable.

    b) The George Washington Bridge across the Hudson River in New York has a span of 3500 feet and a sag of 316 feet. Find an equation for the cable.

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    Quote Originally Posted by Rae View Post
    The shape of a flexible and inelastic cable supporting a load that is uniformly distributed horizontally, like the cables of a suspension bridge, is a parabola.

    a) Place the origin of an xy-coordinate system at the lowest point of a parabolic cable of a suspension bridge whose span is "L" and sag is "h." Find an equation for the cable.

    b) The George Washington Bridge across the Hudson River in New York has a span of 3500 feet and a sag of 316 feet. Find an equation for the cable.

    Thanks
    1. Draw a sketch.

    2. The general equation of the parabola in question is:

    y = a\cdot x^2

    3. The point P\left(\frac12 L\ ,\ h\right) belongs to the parabola.

    4. Plug in the coordinates of P into the equation of the parabola and solve for a:

    h = a\cdot \left(\frac12 L\right)^2~\implies~a=\dfrac{4h}{L}

    5. Use these results to answer b).
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