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Math Help - Drone Aeroplane distance changing at an instant

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    Drone Aeroplane distance changing at an instant

    A drone aeroplane is flying horizontally at a constant height of 4000 ft above a fixed radar tracking station. At a certain instant the angle of elevation theta is 30 degrees and is decreasing, and the speed of the drone aeroplane is 300 mi/h. How fast is the distance between the aeroplane and the radar station changing at this instant? Express the rate in units of ft/s. Use 1 mi=5280 ft
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    Re: Drone Aeroplane distance changing at an instant

    Quote Originally Posted by titansfreak93 View Post
    A drone aeroplane is flying horizontally at a constant height of 4000 ft above a fixed radar tracking station. At a certain instant the angle of elevation theta is 30 degrees and is decreasing, and the speed of the drone aeroplane is 300 mi/h. How fast is the distance between the aeroplane and the radar station changing at this instant? Express the rate in units of ft/s. Use 1 mi=5280 ft
    sketch a diagram?

    let z = straight-line distance between radar site and drone

    let x = horizontal distance between radar site and drone

    let h = plane's altitude (note that the altitude is in feet)

    note when \theta = 30^\circ , z = 2h and x = h\sqrt{3}

    \frac{dx}{dt} = 300 \, mph

    x^2 + h^2 = z^2

    take the time derivative of the above equation, substitute in your known (and calculated) values, and determine \frac{dz}{dt}

    pay attention to units
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