phyhw4 - valdez (vv689) Homework 04 florin (58140) 1 This...

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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 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 that the vector R = A + B makes with the positive x axis is = 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 = 130 . b r a = 180 130 = 50 , so applying the law of cosines, r 2 = a 2 + b 2 2 a b cos = (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 b Applying the law of sines, b sin = r sin sin = b sin r = arcsin parenleftbigg b sin r parenrightbigg = arcsin parenleftbigg 8 sin 50 15 . 4272 parenrightbigg = 23 . 406 ....
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This note was uploaded on 09/26/2010 for the course PHY 58230 taught by Professor Svhets during the Spring '10 term at University of Texas at Austin.

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phyhw4 - valdez (vv689) Homework 04 florin (58140) 1 This...

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