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Math Help - Related Rates

  1. #1
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    Related Rates

    At noon, ship A passes 7 km WEST of a harbour, heading due NORTH at 9 km/h. At 9 a.m., ship B had left the harbour, sailing due NORTH at 6 km/h. Give an expression for d, the distance between the two ships, in terms of t, the number of hours after noon.
    Last edited by gearshifter; November 1st 2008 at 03:18 PM.
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  2. #2
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    Quote Originally Posted by gearshifter View Post
    At noon, ship A passes 7 km WEST of a harbour, heading due NORTH at 9 km/h. At 9 a.m., ship B had left the harbour, sailing due NORTH at 6 km/h. Give an expression for d, the distance between the two ships, in terms of t, the number of hours after noon.
    Use a coordinate system with the harbour at (0, 0), the positive x-axis pointing East and the positive y-axis pointing North.

    Then the position of ship A is:

    A(-7, 9t) and the position of ship B is:

    B(0, 6(t+3))

    Now use the distance formula:

    d=\sqrt{(-7-0)^2+(9t-6(t+3))^2} = \sqrt{9t^2-108t+373}
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