1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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!

  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook