- #1

BigFlorida

- 41

- 1

## Homework Statement

[/B]

A swimmer located at point A needs to reach a point B 20 meters downstream on the opposite bank of a 10 meter wide river. The river flows horizontally at a rate of 0.5 meters/second, and the swimmer has a constant speed of 0.25 meters/second.

Set up the vector equations needed to determine the velocity vector of the swimmer, then determine the velocity vector of the swimmer.

## Homework Equations

Length: ||s|| = sqrt( s

_{1}

^{2}+ ... + s

_{n}

^{2})

## The Attempt at a Solution

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I do not know why this question has given me so much trouble, as all the others have went relatively well. I know that:

*speed is the length of the velocity vector,

*the swimmer's x-component of velocity is (I think) <0.25cos(theta) , 0 > (this is the component for the current, but I know something is not right when I try to take the magnitude and it does not come out as 0.5, but I do not know what else to do to it.)

*the swimmer's y-component of velocity is (I think) <0, 0.25sin(theta)>

*Together, these give the swimmer a velocity, relative to the ground, <0.25cos(theta), 0.25sin(theta)> which seems to be correct when the length is evaluated.

Also, I used the length and width of the river to find the angle. Is all of this wrong? Is there something blatantly obvious that I am missing?

I am just at a loss and have spent hours on this question. Any help would be very much appreciated.