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Math Help - Got this interesting little problem in my test...

  1. #1
    Bar0n janvdl's Avatar
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    Got this interesting little problem in my test...

    And I'd like to know the answer because it's bugging me now


    A kite, 30m above the ground, moves horisontally at a speed of 5m/s.
    At what rate is the angle between the string and the horisontal decreasing when 50m of string has been let out?


    Thanks in advance guys.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by janvdl View Post
    And I'd like to know the answer because it's bugging me now


    A kite, 30m above the ground, moves horisontally at a speed of 5m/s.
    At what rate is the angle between the string and the horisontal decreasing when 50m of string has been let out?


    Thanks in advance guys.
    Let the plan distance from the string holder to the kite be d, assume zero heigh for the ground ebd of the string.

    Then:

     \tan(\theta)=\frac{30}{x}

    differentiate wrt to time:

    (\sec(\theta))^2 \frac{d \theta}{dt}=-\frac{30}{x^2}\frac{dx}{dt}

    and you should be able to do it from there as x'=3 m/s.

    (also the string forms a 30,40,50 m right triangle with the ground and the vertival dropped from the kite.

    RonL
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Let the plan distance from the string holder to the kite be d, assume zero heigh for the ground ebd of the string.

    Then:

     \tan(\theta)=\frac{30}{x}

    differentiate wrt to time:

    (\sec(\theta))^2 \frac{d \theta}{dt}=-\frac{30}{x^2}\frac{dx}{dt}

    and you should be able to do it from there as x'=3 m/s.

    RonL
    Thank you Captain. I did it similarly. Only with cos and i think i left out dx/dt so it will probably be wrong.
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