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Additional Sample Problems - Additional Sample Problems 1...

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Additional Sample Problems 1. Compute the x and y-components of the vectors in Fig. 1.28. Solutions ( 29 ( 29 m. 6 . 9 37.0 cos m 0 . 12 m, 2 . 7 37.0 sin m 0 . 12 ; = = = = y x A A A ( 29 ( 29 ( 29 ( 29 m. 2 . 5 60.0 sin m 0 . 6 m, 0 . 3 60.0 cos m 0 . 6 ; m. 6 . 9 40.0 sin m 0 . 15 m, 5 . 11 40.0 cos m 0 . 15 ; - = - = - = - = - = - = = = y x y x C C B B C B 2. For the vectors in Fig, 1.27, use the method of components to find the magnitude and direction of a) the vector sum ; b) the vector sum ; c) the vector difference ; d) the vector difference . Solutions Using components as a check for any graphical method, the components of B are m 4 . 14 = x B and m, 8 . 10 = y B A has one component, m 12 - = x A . a) The - x and - y components of the sum are 2.4 m and 10.8 m, for a magnitude of ( 29 ( 29 m, 1 . 11 m 8 . 10 m 2.4 2 2 = + , and an angle of . 6 . 77 2.4 10.8 = b) The magnitude and direction of A + B are the same as B + A . c) The x - and y-components of the vector differenceare – 26.4 m and m, 8 . 10 - for a magnitude of m 28.5 and a direction arctan ( 29 . 202 4 . 26 8 . 10 = - - Note that 180 must be added to ( 29 ( 29 22 arctan arctan 4 . 26 8 . 10 4 . 26 8 . 10
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