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Posted by on Saturday, March 12, 2011 at 7:05pm.

A plane flies horizontally with a speed Of 600km/h at an altitude of 10km and pasess directly over th town of quinton .find the rate at which the distance from the plane to quinton is increasing when its 20km away from quinton ?

  • Calculus - , Sunday, March 13, 2011 at 2:07pm

    Not sure why the oblique distance needs to be calculated, but that's what the question asks.
    The solution is similar to the cone problem.

    dx/dt=600 km h-1
    h=10 km
    x=20 km
    L=sqrt(x²+h²)
    dL/dx=x/sqrt(x²+h²)
    dL/dt
    =(dL/dx) * (dx/dt)
    =(x/sqrt(x²+h²)) * (600 km h-1)
    =600x/sqrt(x²+h²) km-h-1
    =537 km-h-1

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