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# hw5 - lavallo(jhl936 Homework 04 orin(58140 This print-out...

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lavallo (jhl936) – Homework 04 – florin – (58140) 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 (part 1 of 2) 10.0 points Two vectors A and B , are lying in the xy plane and given by A = A x i + A y j B = B x i + B y j . where A x = 2 . 67 m, A y = 0 . 979 m, B x = 4 . 2 m, B y = 8 . 58 m. Let R = A + B . Find the magnitude of R . Correct answer: 10 . 2456 m. Explanation: The resultant vector R is given by R = A + B = ( A x i + A y j ) + ( B x i + B y j ) = ( A x + B x ) i + ( A y + B y ) j = (2 . 67 m + 4 . 2 m) i + (0 . 979 m + ( 8 . 58 m)) j = 6 . 87 m i + ( 7 . 601 m) j . The magnitude, R , of R is R = radicalBig R 2 x + R 2 y = radicalBig (6 . 87 m) 2 + ( 7 . 601 m) 2 = 10 . 2456 m . 002 (part 2 of 2) 10.0 points Find the angle θ that the vector R makes from the positive x axis. Choose your answer to be between 180 and +180 . The positive an- gular direction is counter clockwise measured from the x axis. Correct answer: 47 . 8918 . Explanation: The point is in the fourth quadrant of the coordinate system, so the angle θ that the vector R = A + B makes with the positive x axis is θ = arctan R y R x = arctan ( 7 . 601 m) (6 . 87 m) = ( 47 . 8918 ) = 47 . 8918 . 003 (part 1 of 2) 10.0 points Consider two vectors vector A and vector B and their re- sultant vector A + vector B . The magnitudes of the vectors vector A and vector B are, respectively, 14 . 5 and 6 . 1 and they act at 65 to each other. vector A vector B vector A + vector B Find the magnitude of the resultant vector vector A + vector B . Correct answer: 17 . 9505. Explanation: Let : a = 14 . 5 , b = 6 . 1 , and θ = 65 . b γ r a γ = 180 65 = 115 , so applying the law of cosines, r 2 = a 2 + b 2 2 a b cos γ = (14 . 5) 2 + (6 . 1) 2 2 (14 . 5) (6 . 1) cos 115 = 322 . 221 r = 322 . 221 = 17 . 9505 . 004 (part 2 of 2) 10.0 points Find the angle between the direction of the

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lavallo (jhl936) – Homework 04 – florin – (58140) 2 resultant vector A + B and the direction of the vector A . Correct answer: 17 . 9378 . Explanation: a r β γ b Applying the law of sines, b sin β = r sin γ sin β = b sin γ r β = arcsin parenleftbigg b sin γ r parenrightbigg = arcsin parenleftbigg 6 . 1 sin 115 17 . 9505 parenrightbigg = 17 . 9378 . 005 (part 1 of 2) 10.0 points Vector vector A has x and y components of 20 cm and 6 . 7 cm , respectively; vector vector B has x and y components of 19 . 9 cm and 20 cm , respec- tively. If vector A vector B +3 vector C = 0, what is the x component of vector C ?
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hw5 - lavallo(jhl936 Homework 04 orin(58140 This print-out...

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