# OldHW7 - hiarker(srh959 – oldhomework 07 – Turner...

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Unformatted text preview: hiarker (srh959) – oldhomework 07 – Turner – (58220) 1 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 53 m, lie along the sides of a parallelogram as shown in the figure. The angle between vector A and B is 40 ◦ . A 5 3 m C 53 m B 53 m D 5 3 m 40 ◦ What is the magnitude of the vector sum of the four vectors? Correct answer: 199 . 215 m. Explanation: Let : α = 40 ◦ and ℓ = 53 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 (53 m) (1 + cos 40 ◦ ) ˆ ı + 2 (53 m) sin 40 ◦ ˆ = (187 . 201 m) ˆ ı + (68 . 1355 m) ˆ , and R = radicalBig (187 . 201 m) 2 + (68 . 1355 m) 2 = 199 . 215 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 (53 m) cos(20 ◦ ) = 199 . 215 m . 002 10.0 points A novice golfer on the green takes three strokes to sink the ball. The successive dis- placements are 4 . 5 m to the north, 6 . 9 m northeast, and 1 . 9 m 44 ◦ 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: 8 . 76725 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 156.0 m at an angle of 15.0 ◦ below the horizontal. What is the horizontal component of the submarine’s displacement? Correct answer: 150 . 684 m....
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OldHW7 - hiarker(srh959 – oldhomework 07 – Turner...

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