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Math Help - Finding the equation for a word problem

  1. #1
    yoslex
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    Red face Finding the equation for a word problem

    Hey and thanks for looking

    "An airplane is flying at a constant speed and altitude, on a line that will take it direclty over a radar station located on the ground. At the instant that the plane is 600,000 feet from thes tation, an observer in the station notes that its angle of elevation is 30 degree and is increasing at a rate of 0.5 degree per second. Find the speed of the airplane."

    First of all, my question is is there an equation that can relate to the word problem which will allow me to find the speed of the plane using the derivative method?

    Sorry if I'm not clear enough
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by yoslex View Post
    Hey and thanks for looking

    "An airplane is flying at a constant speed and altitude, on a line that will take it direclty over a radar station located on the ground. At the instant that the plane is 600,000 feet from thes tation, an observer in the station notes that its angle of elevation is 30 degree and is increasing at a rate of 0.5 degree per second. Find the speed of the airplane."
    First of all, my question is is there an equation that can relate to the word problem which will allow me to find the speed of the plane using the derivative method?...
    Hi,

    first draw a sketch of the described situation.

    With your values the plane flies at an altitude of 346,410 feet that's nearly ten times the normal altitude of a long ditance flight. (Presumely the observed angle is 3(?))
    The given rate of change leads to a speed of (roughly) 8,155 miles per hour which is ten times the speed too a normal aeroplane is flying.

    The fact that nobody has answered yet indicates that your problem contains some severe mistakes.

    EB

    PS.: I tried to attach a diagram but I cann't upload the file. So sorry.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by yoslex View Post
    Hey and thanks for looking

    "An airplane is flying at a constant speed and altitude, on a line that will take it direclty over a radar station located on the ground. At the instant that the plane is 600,000 feet from thes tation, an observer in the station notes that its angle of elevation is 30 degree and is increasing at a rate of 0.5 degree per second. Find the speed of the airplane."

    First of all, my question is is there an equation that can relate to the word problem which will allow me to find the speed of the plane using the derivative method?

    Sorry if I'm not clear enough
    The elevation puts this aircraft above the effective limit of the atmoshere
    at a height of about >~180km, which puts it in orbit, also means that the
    curvature of the earth cannot be ignored, and probably puts the problem
    beyond the limits of what you have studied.

    An altitude of a tenth of that given would not be implausible (though would
    have to be a millitary or research aircraft - normal cruising heights for civil
    airliners tend to be ~30,000 ft, and smaller aircraft would normally be less
    than that)

    RonL
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