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Unformatted text preview: This print-out should have 16 questions. Multiple-choice 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 one-half 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