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Math Help - The Spotlight: a related rates problem

  1. #1
    Junior Member winterwyrm's Avatar
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    The Spotlight: a related rates problem

    A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.9 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

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  2. #2
    Eater of Worlds
    galactus's Avatar
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    More similar triangles.

    I will post a diagram here in a little bit.

    Similar triangles:

    \frac{y}{12}=\frac{2}{12-x}

    y=\frac{-24}{12-x}

    \frac{dy}{dt}=\frac{24}{(x-12)^{2}}\frac{dx}{dt}

    dx/dt=-1.9 and x=4:

    \frac{dy}{dt}=\frac{24}{(12-4)^{2}}(-1.9)=\frac{-57}{80}\approx{-0.7125} \;\ m/sec
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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