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Math Help - Another Optimization Question

  1. #1
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    Another Optimization Question

    hello, I posted an optimization question earlier and I got another one that I am struggling with. It states:

    A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Is the length of his shadow on the building increasing or decreasing? Find the rate of change of the length of his shadow when he is 4 m from the light.

    Any help will be greatly appreciated!

    thanks a lot!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by dmitri View Post
    hello, I posted an optimization question earlier and I got another one that I am struggling with. It states:

    A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Is the length of his shadow on the building increasing or decreasing? Find the rate of change of the length of his shadow when he is 4 m from the light.

    Any help will be greatly appreciated!

    thanks a lot!
    Why don't you post your work as of now? Here is a hint, this will involve similar triangles.
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  3. #3
    Eater of Worlds
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    Use similar triangles. Draw a diagram.

    \frac{y}{15}=\frac{2}{x}

    y=\frac{30}{x}

    Now, differentiate both sides wrt time, enter in your givens and you're done.
    Last edited by galactus; November 24th 2008 at 05:38 AM.
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