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Help me with the set up! (The distance/speed formulation)

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data
    crossing a river from point A to a point B directly across point A. The river R is 1 mile wide, the swimmer swims at s=5mph and the river is flowing westbound at f=1mph. Find the optimal direction theta to swim in order to reach point B the fastest. This is an optimization problem, but I just need some pointers, as I think m basic formulation is all wrong. Thanks


    2. Relevant equations



    3. The attempt at a solution

    minimize T(theta)=R/(sin(theta)*5)*f-cos(theta)*s*(R/(sin(theta)*s))
     
  2. jcsd
  3. Apr 26, 2010 #2
    this is just relative velocity, convert all your info to si units(unnecessary but a good habit) the shortest distance is obviously straight across. Draw your vector diagrams and find the resultant!
     
  4. Apr 26, 2010 #3
    I get 4.9mp/h at 78.5degrees.
     
  5. Apr 26, 2010 #4
    just curios what are s and f
     
  6. Apr 27, 2010 #5
    s is the swimmer's speed and f is the drift of the river, flowing at a westward direction.
     
  7. Apr 27, 2010 #6
    Actually' I've just realized it really isn't relative velocity. This link gave me good pointers. Thanks for your help, though!

    http://www.janrik.net/mathexpl/swimwalk.html
     
  8. Apr 27, 2010 #7
    the how to and answers i gave you should be correct it may not technically fit under the relative velocity heading but the same techniques are used.
     
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