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Math Help - pully question

  1. #1
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    pully question

    This is another confusing word problem where you need to have a good diagram to work off of.

    A pully is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pully. One end of the rope is tied to the bucket and the other end dangles loosly to the ground. A construction worker holds the end of the rope at a constant height (1.5 m) and walks away from beneath the pully at 1.6 m/s. How fast is the bucket rising when he is 9 m away from the path of the rising cement bucket?

    Can anyone help out with this one? It's really bothering me.
    Thx
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  2. #2
    Eater of Worlds
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    Like many of these related rates problems, it involves ol' Pythagoras.

    Let z=the hypoteneuse of the triangle (the length of the rope).

    By Pythagoras:

    x^{2}+(13.5-1.5)^{2}=z^{2}

    x^{2}+144=z^{2}

    Differentiate:

    2x\frac{dx}{dt}=2z\frac{dz}{dt}

    When x=9, we can see that z=15.

    \frac{dz}{dt}=\frac{x}{z}\frac{dx}{dt}

    \frac{dz}{dt}=\frac{9}{15}(\frac{8}{5})=\frac{24}{  25} \;\ m/sec
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