Physics Help Forum Frame of reference

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Jan 16th 2011, 01:48 PM #1 Junior Member   Join Date: Jan 2011 Posts: 5 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
 Jan 16th 2011, 07:56 PM #2 Senior Member   Join Date: Jul 2009 Location: Kathu Posts: 132 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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