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Math Help - Distance of two moving objects.

  1. #1
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    Distance of two moving objects.

    At noon ship A is 100 km west of ship B. Ship A travels south at 35km/h and ship B travels North at 25 km/hr. At 4pm how fast does the distance between them change?

    I don't quite understand how to do this so a complete explanation would be best.
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  2. #2
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    Haha, I have nearly the same problem.

    This has to do with implicit differentiation

    Use the formula d = v*t


    I would say you could also use a^2+b^2=c^2 but they're going in complete opposite directions.

    By the way your problem is featured on youtube.

    Last edited by Zanderist; March 18th 2010 at 04:53 AM.
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  3. #3
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    Quote Originally Posted by Neversh View Post
    At noon ship A is 100 km west of ship B. Ship A travels south at 35km/h and ship B travels North at 25 km/hr. At 4pm how fast does the distance between them change?

    I don't quite understand how to do this so a complete explanation would be best.
    Set up a coordinate system so that ship A is at (0, 0) and ship B is at (100, 0). t hours after noon, ship A is at (0, -35t) and ship B is at (100, 25t).

    The distance between them, as a function of t, is \sqrt{100^2+ (25t-(-35t))^2}= \sqrt{100^2+ 60^2t^2}.

    Find the derivative of that at t= 4.
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