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

1. Apr 26, 2010

### koosy

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. Apr 26, 2010

### pat666

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!

3. Apr 26, 2010

### pat666

I get 4.9mp/h at 78.5degrees.

4. Apr 26, 2010

### pat666

just curios what are s and f

5. Apr 27, 2010

### koosy

s is the swimmer's speed and f is the drift of the river, flowing at a westward direction.

6. Apr 27, 2010

### koosy

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

7. Apr 27, 2010

### pat666

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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