Chap3 - 15(a Strategy Since the angle is below the x-axis...

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15. (a) Strategy Since the angle is below the + x -axis, it is negative. Solution Compute the components. 7.1cos( 14 ) 6.9 and 7.1sin( 14 ) 1.7 . x y B B = ° = = ° = y x 7.1 B C x = - 1.8 C y = - 6.7 14° (b) Strategy The components of C r are given. Use the Pythagorean theorem. Solution Compute the magnitude and direction of . C r 2 2 2 2 1 ( 1.8) ( 6.7) 6.9 6.7 tan 15 CW from the -axis 1.8 x y C C C y θ = + = + − = = = ° (c) Strategy Add the components of the vectors to find the components of the vector sum. Use the Pythagorean theorem. Give the angle with respect to the axis to which it lies closest. Solution Find the magnitude and direction of . + C B r r 2 2 2 2 ( ) ( ) ( 1.8 6.9) ( 6.7 1.7) 9.8 x x y y C B C B + = + + + = + + − = C B r r and 1 8.4 tan 31 CCW from the -axis . 5.1 y θ = = ° (d) Strategy Use the components of and C B r r to find those of . C B r r Solution Compute the magnitude and direction. 2 2 2 2 1 ( ) ( ) ( 1.8 6.9) [ 6.7 ( 1.7)] 10 5.0 tan 30 CCW from the -axis 8.7 x x y y C B C B x θ = + = + − − − = = = ° C B r r (e) Strategy Use the components of
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