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Unformatted text preview: lenoir (wml297) – oldhomework 07 – Turner – (58220) 1 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 59 m, lie along the sides of a parallelogram as shown in the figure. The angle between vector A and B is 73 ◦ . A 5 9 m C 59 m B 59 m D 5 9 m 73 ◦ What is the magnitude of the vector sum of the four vectors? Correct answer: 189 . 71 m. Explanation: Let : α = 73 ◦ and ℓ = 59 m . The vectors are vector B = vector C = ℓ ˆ ı and vector A = vector D = ( ℓ cos α ) ˆ ı + ( ℓ sin α ) ˆ , so vector A + vector B + vector C + vector D = 2 ℓ (1 + cos α )ˆ ı + 2 ℓ sin α ˆ = 2 (59 m) (1 + cos 73 ◦ ) ˆ ı + 2 (59 m) sin73 ◦ ˆ = (152 . 5 m) ˆ ı + (112 . 844 m) ˆ , and R = radicalBig (152 . 5 m) 2 + (112 . 844 m) 2 = 189 . 71 m . Alternate Solution: Rotate the figure clockwise by 1 2 α . The resultant 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 cos parenleftBig α 2 parenrightBig , so R = 4 ℓ cos parenleftBig α 2 parenrightBig = 4 (59 m) cos (36 . 5 ◦ ) = 189 . 71 m . 002 10.0 points A novice golfer on the green takes three strokes to sink the ball. The successive dis placements are 7 . 2 m to the north, 6 . 6 m northeast, and 5 . 6 m 45 ◦ 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: 7 . 93866 m. 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 ◦ so, the magnitude of d is:  d  = radicalBig d 2 x + d 2 y 003 (part 1 of 2) 10.0 points A submarine dives 191.0 m at an angle of 14.0 ◦ below the horizontal. What is the horizontal component of the submarine’s displacement? Correct answer: 185 . 326 m. Explanation: lenoir (wml297) – oldhomework 07 – Turner – (58220) 2 Let : d = 191 . 0 m and θ = − 14 ....
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 Spring '10
 Turner
 Vector Space, Correct Answer, Vector Motors, D2, Lenoir

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