I'm stuck trying to figure out how I can find out the magnitude of vA and vB when I have the magnitude of vTOT which is vA+vB
I know that the sum of them, vTOT has a speed of 4.5 m/s and speed is the same thing as magnitude pretty much for my purposes in this problem. But I don't know how to use these angles and the other given information to figure out the magnitudes of vA and vB
Best Answer
Use the Sine Law of triangles: In triangle with sides of length $a_1,a_2,a_3$ that are opposite to angles $A_1,A_2,A_3$ we have $$a_1/\sin A_1=a_2/\sin A_2=a_3/\sin A_3.$$ The 3rd angle in the green triangle is $180^o-30.8^o-18.1^o=131.1^o.$ Therefore $$|v_{tot}|/\sin 131.1^o=|v_A|/\sin 18.1^o=|v_B|/\sin 30.8^o.$$