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Math Help - calculus AB help with related rates

  1. #1
    Newbie ballet_dansur13's Avatar
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    Question calculus AB help with related rates

    A hot-air balloon is rising straight up from a level field and is tracked by a range finder 500 ft from lift-off point. the balloon rises at a rate of 15 feet per second.

    A) How fast is the direct distance between the range finder and the ballon changing at 5 seconds

    B) how fast is the angle of elevation changing when the ballon is 500 feet high


    he gave us a diagram of a right trianle with the hypotenus labeled d and the side labled h and the bottom equalling 500

    i think i solved part a and i got 2.223 ft but i wasn't sure how to do part b
    any help is appreciated
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  2. #2
    MHF Contributor kalagota's Avatar
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    get an equation relating the angle with the given data. and since it is a right triangle, you can use SOHCAHTOA.. in fact, you'll just need TOA.
    Last edited by kalagota; May 22nd 2008 at 06:51 AM.
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  3. #3
    Eater of Worlds
    galactus's Avatar
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    Part a looks good. Good work.

    For part b, use tangent. I will get you started:

    tan({\theta})=\frac{y}{500}

    Differentiate:

    sec^{2}({\theta})\frac{d{\theta}}{dt}=\frac{1}{500  }\frac{dy}{dt}

    You know dy/dt. Find theta when y=75 and you're set.
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