Solutions01 - Physics 140 - Discussion 01 - Solutions 1.42....

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Physics 140 - Discussion 01 - Solutions 1.42. I DENTIFY : Find A and B . Find the vector difference using components. S ET U P : Deduce the x - and y -components and use Eq. (1.8). E XECUTE : (a) ˆ ˆ 4.00 7.00 ; = + r A i j A x = + 4.00; 7.00. y A = + 2 2 2 2 (4.00) (7.00) 8.06. x y A A A = + = + = ˆ ˆ 5.00 2.00 ; = - r B i j B x = + 5.00; 2.00; y B = - 2 2 2 2 (5.00) ( 2.00) 5.39. x y B B B = + = + - = E VALUATE : Note that the magnitudes of r A and r B are each larger than either of their components. E XECUTE : (b) ˆ ˆ ˆ ˆ ˆ ˆ 4.00 7.00 (5.00 2.00 ) (4.00 5.00) (7.00 2.00) . - = + - - = - + + A B i j i j i j r r ˆ ˆ 1.00 9.00 - = - + r r A B i j (c) Let ˆ ˆ 1.00 9.00 . - = - + = r r r R A B i j Then R x = - 1.00, R y = 9.00. R = R x 2 + R y 2 R = ( - 1.00) 2 + (9.00) 2 = 9.06. tan θ = R y R x = 9.00 - 1.00 = - 9.00 = - 83.6 ° + 180 ° = 96.3 ° . Figure 1.42 E VALUATE : R x < 0 and 0, y R so r R is in the 2nd quadrant. ______________________________________________________________________________
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Solutions01 - Physics 140 - Discussion 01 - Solutions 1.42....

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