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calculus

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At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 23 knots. How fast (in knots) is the distance between the ships changing at 3 PM?

  • calculus - ,

    Let the distance between them be D n miles.
    Let the time passes since noon be t hours.

    Did you make a diagram?
    I see a right-angles triangle with sides
    (23t), (17t + 30) and D so that
    D^2 = (23t)^2 + (17t + 30)^2

    2D(dD/dt) = 2(23t)(23) + 2(17t+30)(17)
    dD/dt = (529t + 289t + 510)/D

    when t = 3, (3:00 pm)
    D^2 = 4761+6561
    D = 106.405

    dD/dt = (529(3) + 289(3) +510)/106.405
    = 27.86 knots

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