Optimal Direction for Long-Distance Swimmer in Ocean Currents

[Mdhiggenz]

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

 

[Delphi51]

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.