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An observer is located on the ground 6 kilometers from the point where a space shuttle is launched (vertically). When the shuttle is 8 kilometers high, it is travelling at 500 kilometers per hour. Determine, for that moment, the rate at which the distance between the observer and the shuttle is changing.

  • math -

    draw a diagram. The distance from the observer to the shuttle when the height is y, is

    d^2 = 6^2 + y^2

    2d dd/dt = 2y dy/dt

    when y=8, d=10 so

    20 dd/dt = 2(8)(500)
    dd/dt = 400 km/hr

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