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math cal

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A plane flying horizontally at an altitude of 3 mi and a speed of 480 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. (Round to the nearest whole number.)

  • math cal - ,

    Did you make a sketch and got a right-angled triangle?
    let the horizontal distance between the plane and the station be x miles
    let the distance between the plane and the station be y miles
    given: dx/dt = 480 mph
    find: dy/dt when y = 6

    y^2 = x^2 + 3^2
    when y = 6
    36 = x^2 + 9
    x = √27

    2y dy/dt = 2x dx/dt
    dy/dt = (x/y)dx/dt
    = √27(480)/6
    = 415.7 mph or 416 mph

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