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Math Help - Related rates question.

  1. #1
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    Related rates question.

    I got 356.84 km/hr for the question below, do you think this is correct?

    A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30. At what rate is the distance from the plane to the radar station increasing a minute later?

    Here is my work:

    dx/dt=360

    y^2=x^2+3^2-2(3)(x)cos120degrees
    =x^2+9-6x(-1/2)
    =x^2+3x+9

    2y dy/dt= 2x dx/dt + dx/dt
    dy/dt= (2x+1)/2y dx/dt

    dy/dt= (13/2y) *360

    x= 360/60= 6 km

    dy/dt= 2(6)+ 3/2 sqrt 43 *360
    = (13/2sqrt 43) *360= 356.84 km/hr
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  2. #2
    Junior Member
    Joined
    Apr 2010
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    Quote Originally Posted by ioke09 View Post
    I got 356.84 km/hr for the question below, do you think this is correct?

    A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30. At what rate is the distance from the plane to the radar station increasing a minute later?

    Here is my work:

    dx/dt=360

    y^2=x^2+3^2-2(3)(x)cos120degrees
    =x^2+9-6x(-1/2)
    =x^2+3x+9

    2y dy/dt= 2x dx/dt + dx/dt<--- 2y dy/dt= 2x dx/dt + 3 dx/dt
    dy/dt= (2x+1)/2y dx/dt

    dy/dt= (13/2y) *360

    x= 360/60= 6 km

    dy/dt= 2(6)+ 3/2 sqrt 43 *360
    = (13/2sqrt 43) *360= 356.84 km/hr
    Just a small mistake in taking the derivative otherwise you are doing it correctly.
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