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# phyhw4 - valdez(vv689 – Homework 04 – florin –(58140...

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Unformatted text preview: valdez (vv689) – 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 = 9 . 46 m, A y = 2 . 04 m, B x = 9 . 15 m, B y = − 4 . 14 m. Let R = A + B . Find the magnitude of R . Correct answer: 18 . 7281 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 = (9 . 46 m + 9 . 15 m) i + (2 . 04 m + ( − 4 . 14 m)) j = 18 . 61 m i + ( − 2 . 1 m) j . The magnitude, R , of R is R = radicalBig R 2 x + R 2 y = radicalBig (18 . 61 m) 2 + ( − 2 . 1 m) 2 = 18 . 7281 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: − 6 . 43817 ◦ . 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 ( − 2 . 1 m) (18 . 61 m) = ( − 6 . 43817 ◦ ) = − 6 . 43817 ◦ . 003 (part 1 of 2) 10.0 points Consider two vectors vector A and vector B and their resul- tant vector A + vector B . The magnitudes of the vectors vector A and vector B are, respectively, 19 . 3 and 8 and they act at 130 ◦ to each other. vector A vector B vector A + vector B Find the magnitude of the resultant vector vector A + vector B . Correct answer: 15 . 4272. Explanation: Let : a = 19 . 3 , b = 8 , and θ = 130 ◦ . b γ r a γ = 180 ◦ − 130 ◦ = 50 ◦ , so applying the law of cosines, r 2 = a 2 + b 2 − 2 a b cos γ = (19 . 3) 2 + (8) 2 − 2 (19 . 3) (8) cos 50 ◦ = 237 . 997 r = √ 237 . 997 = 15 . 4272 . 004 (part 2 of 2) 10.0 points Find the angle between the direction of the resultant vector A + B and the direction of the vector A . Correct answer: 23 . 406 ◦ . valdez (vv689) – Homework 04 – florin – (58140) 2 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 8 sin 50 ◦ 15 . 4272 parenrightbigg = 23 . 406 ◦ ....
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phyhw4 - valdez(vv689 – Homework 04 – florin –(58140...

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