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Old Jan 16th 2011, 02:48 PM   #1
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Join Date: Jan 2011
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Frame of reference

I'm having trouble deciding on which laws to use to calculate the final velocity.

Where:
s = swimmer
w = water
b = beach(ground)

sVw = 4m/s [N]
wVb = 2m/s[E 25 S]

I tried using sVb^2 = sVw^2 + wVb^2 - 2(sVw)(wVb)cos(65) giving me 3.64 m/s. I don't think this is right, but it's the closest I can think of.

To get the angle I tried sin(0-sigma)=((wVb)sin(65))/sVb. It gave me an angle of 30, which is the same as when I tried normal sin law for a right angle.

I think I've over-thought this and caused myself more trouble than it was worth lol
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Old Jan 16th 2011, 08:56 PM   #2
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Frame of reference

avengefulghost,

Although you might have used a longer method, your answer is still correct. Assuming that E25S means 25 degrees S of east or 115 degrees then it is simply a case of breaking each vector into its components

Running x=4, y=0
Swimming x = -0.85, y = 1.81
Combined (Add X's and Y's) x = 3.15 , y = 1.81
Magnitude of the final velocity = SQRT(X^2+Y^2) = 3.64
Bearing of the final velocity (X = N) = ArcCos(3.15/3.64) = 29.88 degrees which is what you got.

The recipe is to break the components down into the x's and y's, add the x's and y's, use pythagoras to find the magnitude and then apply trigonometry to get the bearing. Bearings can be a bit tricky but normally the convention is to take it clockwise with zero being north unless you are told differently.
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