Spring 2010 - HW04_Solution

# Spring 2010 - HW04_Solution - banuelos(ojb93 Homework 04...

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banuelos (ojb93) – Homework 04 – forin – (58140) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – Fnd all choices be±ore answering. 001 (part 1 o± 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 = 3 . 17 m, A y = 0 . 356 m, B x = 3 . 08 m, B y = 6 . 38 m. Let R = A + B . ²ind the magnitude o± R . Correct answer: 8 . 6805 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 = (3 . 17 m + 3 . 08 m) i + (0 . 356 m + ( 6 . 38 m)) j = 6 . 25 m i + ( 6 . 024 m) j . The magnitude, R , o± R is R = r R 2 x + R 2 y = r (6 . 25 m) 2 + ( 6 . 024 m) 2 = 8 . 6805 m . 002 (part 2 o± 2) 10.0 points ²ind the angle θ that the vector R makes ±rom the positive x axis. Choose your answer to be between 180 and +180 . The positive an- gular direction is counter clockwise measured ±rom the x axis. Correct answer: 43 . 9452 . Explanation: The point is in the ±ourth quadrant o± 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 ( 6 . 024 m) (6 . 25 m) = ( 43 . 9452 ) = 43 . 9452 . 003 (part 1 o± 2) 10.0 points Consider two vectors v A and v B and their re- sultant v A + v B . The magnitudes o± the vectors v A and v B are, respectively, 19 . 4 and 6 . 2 and they act at 51 to each other. v A v B v A + v B ²ind the magnitude o± the resultant vector v A + v B . Correct answer: 23 . 7947. Explanation: Let : a = 19 . 4 , b = 6 . 2 , and θ = 51 . b γ r a γ = 180 51 = 129 , so applying the law o± cosines, r 2 = a 2 + b 2 2 a b cos γ = (19 . 4) 2 + (6 . 2) 2 2 (19 . 4) (6 . 2) cos 129 = 566 . 189 r = 566 . 189 = 23 . 7947 . 004 (part 2 o± 2) 10.0 points ²ind the angle between the direction o± the resultant vector A + B and the direction o± the vector A . Correct answer: 11 . 6829 . Explanation:

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banuelos (ojb93) – Homework 04 – forin – (58140) 2 a r β γ b Applying the law oF sines, b sin β = r sin γ sin β = b sin γ r β = arcsin p b sin γ r P = arcsin p 6 . 2 sin 129 23 . 7947 P = 11 . 6829 . 005 (part 1 oF 2) 10.0 points Vector v A has x and y components oF 20 cm and 2 . 6 cm , respectively; vector v B has x and y components oF 16 . 6 cm and 20 cm , respec- tively.
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Spring 2010 - HW04_Solution - banuelos(ojb93 Homework 04...

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