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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: α = 59 ◦ and ℓ = 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) ˆ ı vector A = vector D = (89 m) (cos A ) ˆ ı + (89 m)(sin α ) ˆ Thus, vector A + vector B + vector C + vector D = 2 [ ℓ ı + ℓ cos α ˆ ı ] + 2 [ ℓ sin α ˆ ] = 2 [(89 m) ı + (89 m) cos(59 ◦ ) ˆ ı ] + 2 [(89 m) sin(59 ◦ ) ˆ ] = (269 . 677 m) ı + (152 . 576 m) ˆ , 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 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 ℓ times the cosine of the half angle. R = 4 ℓ cos parenleftBig α 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 ˆ ı + d y ˆ 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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 Spring '08
 Turner
 Trigonometry, Addition, Vector Space, Correct Answer, Vector Motors

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