oldhw7_s - oldhomewk 07 YOO, HEE Due: Jan 31 2008, 4:00 am...

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Unformatted text preview: oldhomewk 07 YOO, HEE Due: Jan 31 2008, 4:00 am 1 Question 1, chap 3, sect 3. part 1 of 1 10 points Four vectors, each of magnitude 89 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 8 9 m C 89 m B 89 m D 8 9 m 59 What is the magnitude of the vector sum of the four vectors? Correct answer: 309 . 847 m (tolerance 1 %). Explanation: = 59 and = 89 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 = (89 m) vector A = vector D = (89 m) (cos A ) + (89 m)(sin ) Thus, vector A + vector B + vector C + vector D = 2 [ + cos ] + 2 [ sin ] = 2 [(89 m) + (89 m) cos(59 ) ] + 2 [(89 m) sin(59 ) ] = (269 . 677 m) + (152 . 576 m) , where R x = 269 . 677 m and R y = 152 . 576 m . The magnitude of the vector sum is R = radicalBig R 2 x + R 2 y = radicalBig (269 . 677 m) 2 + (152 . 576 m) 2 = 309 . 847 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 (89 m) cos (29 . 5 ) = 309 . 847 m . Question 2, chap 3, sect 3. part 1 of 1 10 points A novice golfer on the green takes three strokes to sink the ball. The successive dis- placements are 5 . 2 m to the north, 8 . 4 m northeast, and 3 . 6 m 71 west of south. Start- ing at the same initial point, an expert (lucky) golfer could make the hole in a single displace- ment. What is the magnitude of this single dis- placement? Correct answer: 10 . 2852 m (tolerance 1 %). 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 oldhomewk 07 YOO, HEE Due: Jan 31 2008, 4:00 am 2 so, the magnitude of d is: | d | = radicalBig d 2 x + d 2 y Question 3, chap 3, sect 3....
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oldhw7_s - oldhomewk 07 YOO, HEE Due: Jan 31 2008, 4:00 am...

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