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Math Help - Airplanes

  1. #1
    Mar 2008

    Exclamation Airplanes

    An airplane is flying at an altitude of 6 miles and passes directly over a radar antenna. When the plane is 10 miles away, the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane?

    The teacher I have loves planes and assigned this problem and many others. I sloved most of them. Thanks for the time
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Feb 2008
    Yuma, AZ, USA
    by the pythagorean theorem we know that

    6^2+x^2=s^2 and we want to find \frac{dx}{dt} when x=10.

    using the above we know that s=\sqrt{136} when x=10.

    taking the derivative with respect to time

    2x\frac{dx}{dt}=2s\frac{ds}{dt} \iff \frac{dx}{dt}=\frac{s}{x}\frac{ds}{dt}=\frac{\sqrt  {136}}{10}\frac{240 \mbox{ miles}}{\mbox{ hr}}=48\sqrt{34}\frac{miles}{hr}
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