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Unformatted text preview: This printout should have 16 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Four vectors, each of magnitude 58 m, lie along the sides of a parallelogram as shown in the figure. The angle between vector A and B is 59 . Hint: Remember you are adding four vec tors. A 5 8 m C 58 m B 58 m D 5 8 m 59 What is the magnitude of the vector sum of the four vectors? Correct answer: 201 . 923 m. Explanation: = 59 and = 58 m . Basic Concepts: The components of a vector vector R = vector A + vector B + vector C + vector D are obtained by adding up the respective com ponents of each vector in the sum. Solution: vector B = vector C = (58 m) vector A = vector D = (58 m) (cos A ) + (58 m)(sin ) Thus, vector A + vector B + vector C + vector D = 2 [ + cos ] + 2 [ sin ] = 2 [(58 m) + (58 m) cos(59 ) ] + 2 [(58 m) sin(59 ) ] = (175 . 744 m) + (99 . 4314 m) , where R x = 175 . 744 m and R y = 99 . 4314 m . The magnitude of the vector sum is R = radicalBig R 2 x + R 2 y = radicalBig (175 . 744 m) 2 + (99 . 4314 m) 2 = 201 . 923 m . Alternative Solution: Rotate your figue clockwise by onehalf the angle between vec tors A and B . The resulant vector must lie along the horizontal line connecting the tails of vectors A and B and the heads of vectors C and D . The four components along this line are times the cosine of the half angle. R = 4 cos parenleftBig 2 parenrightBig = 4 (58 m) cos (29 . 5 ) = 201 . 923 m . keywords: 002 10.0 points A novice golfer on the green takes three strokes to sink the ball. The successive dis placements are 1 m to the north, 1 . 4 m north east, and 7 m 65 west of south. Starting at the same initial point, an expert (lucky) golfer could make the hole in a single displacement. What is the magnitude of this single dis placement? Correct answer: 5 . 44107 m. Explanation: Take the sum of these three displacements: d = d 1 + d 2 + d 3 = d x + d y where d x = d 2 cos 45 d 3 sin30 d y = d 1 + d 2 sin45 d 3 cos 30 so, the magnitude of d is:  d  = radicalBig d 2 x + d 2 y oldhomework 07 Turner (58185) 1 003 (part 1 of 2) 10.0 points A submarine dives 191 . 0 m at an angle of 14 ....
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This note was uploaded on 03/26/2010 for the course PHY 303K taught by Professor Turner during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Turner
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