PHY303k_-_Spring_2010_-_HW_4

PHY303k_-_Spring_2010_-_HW_4 - saldana(avs387 – Homework...

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Unformatted text preview: saldana (avs387) – 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 = 5 . 86 m, A y = 0 . 196 m, B x = 2 . 58 m, B y = − 9 . 21 m. Let R = A + B . Find the magnitude of R . Correct answer: 12 . 3485 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 = (5 . 86 m + 2 . 58 m) i + (0 . 196 m + ( − 9 . 21 m)) j = 8 . 44 m i + ( − 9 . 014 m) j . The magnitude, R , of R is R = radicalBig R 2 x + R 2 y = radicalBig (8 . 44 m) 2 + ( − 9 . 014 m) 2 = 12 . 3485 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: − 46 . 8836 ◦ . 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 ( − 9 . 014 m) (8 . 44 m) = ( − 46 . 8836 ◦ ) = − 46 . 8836 ◦ . 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, 18 . 1 and 6 . 9 and they act at 53 ◦ to each other. vector A vector B vector A + vector B Find the magnitude of the resultant vector vector A + vector B . Correct answer: 22 . 9247. Explanation: Let : a = 18 . 1 , b = 6 . 9 , and θ = 53 ◦ . b γ r a γ = 180 ◦ − 53 ◦ = 127 ◦ , so applying the law of cosines, r 2 = a 2 + b 2 − 2 a b cos γ = (18 . 1) 2 + (6 . 9) 2 − 2 (18 . 1) (6 . 9) cos 127 ◦ = 525 . 541 r = √ 525 . 541 = 22 . 9247 . 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: 13 . 9088 ◦ . saldana (avs387) – 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 6 . 9 sin 127 ◦ 22 . 9247 parenrightbigg = 13 . 9088 ◦ ....
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PHY303k_-_Spring_2010_-_HW_4 - saldana(avs387 – Homework...

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