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6 - hernandez(ejh742 oldhomework 06 Turner(58120 This...

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hernandez (ejh742) – oldhomework 06 – Turner – (58120) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A quarterback takes the ball from the line of scrimmage, runs backward for 13 yards, then runs sideways parallel to the line of scrim- mage for 10 yards. At this point, he throws a 32 yards forward pass straight downfield perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant displacement? Correct answer: 21 . 4709 yards. Explanation: Let the x direction be parallel to line of scrimmage. Given : Δ y 1 = - 13 yards , Δ x = ± 10 yards , and Δ y 2 = 32 yards . Δ y tot = Δ y 1 + Δ y 2 = - 13 yards + 32 yards = 19 yards Δ x tot = Δ x = ± 10 yards The displacements are perpendicular, so d = radicalBig x tot ) 2 + (Δ y tot ) 2 = radicalBig ( ± 10 yards) 2 + (19 yards) 2 = 21 . 4709 yards . 002 (part 1 of 5) 10.0 points A commuter airplane starts from an airport located at the origin. First it flies to city A located 99 km away from the airport in a direction 32 North of East. Next it flies 61 . 4 km at 31 West of North to city B. Finally it flies 150 km due West to city C. A B C O a c b r α β γ N N E W What is the x -component of the vector vector b ? Consider E to be the positive x axis and N to be the positive y axis. 1. b x = b cos β 2. b x = - b sin β correct 3. b x = - b tan β 4. b x = b tan β 5. b x = b sin β 6. b x = - b cos β Explanation: Let : b = 61 . 4 km and β = 31 . For vectorv = ( v x , v y ) and vectoru = ( u x , u y ) , vectorr = vectoru + vectorv = ( v x + u x , v y + u y ) b β | b x | | b y | Also, for β < 90 (as in this problem), vector b is in the second quadrant; i.e. , its x component is negative and its y component positive: b x = - b sin β = - (61 . 4 km) sin 31 = - 31 . 6233 km .
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