Optimal Direction for Long-Distance Swimmer in Ocean Currents

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SUMMARY

The optimal direction for a long-distance swimmer to cross from Port Angeles, WA, to Victoria, B.C., while accounting for a 3 km/h eastward ocean current, is 49 degrees from due north. The swimmer's speed in still water is 4 km/h. To determine this angle, one must utilize a velocity vector diagram that combines the swimmer's velocity vector with the current's velocity vector to achieve a resultant vector directed straight north. The solution can be derived using the law of sines or the law of cosines, or by resolving the vectors into their x and y components.

PREREQUISITES
  • Understanding of vector components and vector addition
  • Familiarity with the law of sines and law of cosines
  • Basic knowledge of swimming dynamics in current
  • Ability to perform algebraic calculations involving trigonometric functions
NEXT STEPS
  • Study vector addition in physics to understand resultant vectors
  • Learn about the law of sines and law of cosines in trigonometry
  • Research the effects of ocean currents on swimming and navigation
  • Practice solving similar problems involving velocity vectors and angles
USEFUL FOR

Mathematics students, physics enthusiasts, long-distance swimmers, and anyone interested in navigation through currents will benefit from this discussion.

Mdhiggenz
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Homework Statement



A long-distance swimmer is able to swim through still water at 4 km/h. She wishes to try to swim from Port Angeles, WA, due north to Victoria, B.C., a distance of 50 km. An ocean current flows through the Strait of Juan de Fuca from west to east at 3 km/h. In what direction should she swim to make the crossing along a straight line between the two cities?


Homework Equations





The Attempt at a Solution



So I know I have to split it into its x and y components , however I have no idea how to start this problem.

The answer is 49 degrees
 
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You need a velocity vector diagram showing the swimmer vector plus the current vector equaling a combined velocity vector straight north. You can solve the triangle with law of sines, law of cosines to find the swimmer velocity. Or solve it with x,y components and some algebra.
 

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