71_Physics ProblemsTechnical Physics

71_Physics ProblemsTechnical Physics - 72 *P3.56 Vectors 3...

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72 Vectors *P3.56 Let A represent the distance from island 2 to island 3. The displacement is A = A at 159 ° . Represent the displacement from 3 to 1 as B = B at 298 ° . We have 4.76 km at 37 ° ++= AB 0. For x -components 476 37 159 298 0 3 80 0 934 0 469 0 810 199 . cos cos cos .. . km km km a f °+ °+ °= −+= =− + BA For y -components, 0 2 86 0 358 0 883 0 . sin sin sin . km km af °+ °+ +−= N B 28° A C 69° 37° 1 2 3 E FIG. P3.56 (a) We solve by eliminating B by substitution: 2 86 0 358 0 883 8 10 1 99 0 2 86 0 358 7 15 1 76 0 10 0 1 40 717 . . km km km km km km +− += ++ = = = AA A A (b) B = +( ) = 8 10 1 99 7 17 6 15 . . km km km *P3.57 (a) We first express the corner’s position vectors as sets of components Aij i j Bij i j = = 10 50 10 50 6 43 12 30 12 30 10 4
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