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Boats boats boats

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    A boat leave a dock at noon and heads weat at a speed 25km/h. Another boat heads north at 20km/h and reaches the same dock at 1:00 pm. when were the boats closest to each other?


    2. Relevant equations
    when were the boats closest to each other?



    3. The attempt at a solution
    I use the pythagorean for the distance
    but I'm not sure about how to sub them in?
    I tried to assume that the second boat also leaves at noon, so the total distance will be 20km. But thats wrong. Please help, thanks =P[/b]
     
  2. jcsd
  3. Mar 29, 2009 #2
    d(distance)/dt = 0

    Calculate the following quantities in order. All but the last one are functions of time:
    1. the vector position of each boat
    2. the vector distance between the boats
    3. the magnitude of that distance
    4. the time derivative of that magnitude
    5. the time at which that derivative is zero
    As long as the distance between the boats varies smoothly in time, its time derivative will be zero when the distance is at a minimum.
     
  4. Mar 29, 2009 #3
    At t = 0, the first boat has already traveled 25 km.

    So, at any t > 0

    dist btw. them ^ 2 = distance covered by boat 2 ^ 2 + (distance by 1 + 25 ) ^ 2

    You need to differentiate this equation to get speeds in it.

    A diagram about the situation would be a big help.
     
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