What is the Swimmer's Velocity Relative to the Observers on the Beach?

AI Thread Summary
The discussion revolves around calculating a swimmer's velocity relative to observers on the beach, given her velocity of 4 m/s north and a cross current of 2 m/s at an angle of 25 degrees south of east. The initial attempt involved converting polar coordinates to Cartesian coordinates, leading to confusion about whether to assume a right triangle. Participants suggest that using polar-to-Cartesian conversion is a standard method for solving such problems, while also mentioning the law of cosines and sines as alternative approaches. There is a request for clarification on the calculations, particularly regarding the signs of the numbers used. The conversation emphasizes the importance of correctly applying vector addition to determine the swimmer's actual velocity.
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Homework Statement



In an anniversary celebration of Marilyn Bell's 1954 crossing of Lake Ontario a swimmer set out from the shores of New York and maintained a velocity of 4m/s [N]. As the swimmer approached the Ontario shore, she encountered a cross current of 2m/s [E 25deg S]. Find her velocity with respect to the crowd observing from the beach.

The Attempt at a Solution



Firstly, am I to understand that this is a right-angle triangle? When representing it graphically, it certainly does not look like a right triangle:

http://i543.photobucket.com/albums/gg464/yowatupguystill/vector.jpg

However, when I endeavor to solve this by converting from polar to cartesian co-ordinates, it seems that I have to assume a right-triangle.

Let S be the swimmer, W be the water, and G the ground.

sVw = 4 m/s [N] = (4, 90*)
wVg = 2 m/s [E25*S] = (2, -335*)
sVg = ?
.: sVg = sVw + wVg
= [0, 4] + [1.8, 0.84]
= [1.8, 4.84]
= (5.2, 69.5*)

I am not very confident in my answer. For starters, I am not supposed to really solve this using polar-cartesian conversion, but I was at a standstill when attempting another solution. Any light shed on a solution for this would be much appreciated.
 
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[1.8, 0.84]

Double-check the +/- signs in those numbers. Things look fine otherwise.

I am not supposed to really solve this using polar-cartesian conversion ...
That's weird, because that is by far the standard and preferred way to solve problems like this. Alternatively, but more cumbersome, is to use the law of cosines and law of sines from trig.
 
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