How Do You Calculate the Optimal Swimming Angle to Cross a River Quickly?

[koosy]

Homework Statement

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

Homework Equations

The Attempt at a Solution

minimize T(theta)=R/(sin(theta)*5)*f-cos(theta)*s*(R/(sin(theta)*s))

 

[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!

 

[pat666]

I get 4.9mp/h at 78.5degrees.

 

[pat666]

just curios what are s and f

 

[koosy]

just curios what are s and f

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

 

[koosy]

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!

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

 

[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.