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

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Homework Help Overview

The problem involves calculating the optimal swimming angle to cross a river quickly, given specific parameters such as the width of the river, the swimmer's speed, and the river's current. The context is rooted in optimization within the subject area of physics, particularly focusing on relative motion and vector analysis.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formulation of the problem, with one suggesting the use of vector diagrams to analyze the swimmer's path. There is also mention of converting units for clarity and a focus on the swimmer's speed and the river's current as key variables.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning the initial setup. Some have offered guidance on drawing vector diagrams and considering relative motion, while others are exploring the implications of the swimmer's speed and the river's flow. There is a lack of consensus on the best approach, but several lines of reasoning are being explored.

Contextual Notes

Participants note the importance of understanding the definitions of variables such as the swimmer's speed and the river's current. There is also a mention of potential confusion regarding the classification of the problem as relative velocity.

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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))
 
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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!
 
I get 4.9mp/h at 78.5degrees.
 
just curios what are s and f
 
pat666 said:
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.
 
pat666 said:
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
 
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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