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SOL2 - Thevalingam Donald Homework 2 Due 4:00 pm Inst...

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Thevalingam, Donald – Homework 2 – Due: Sep 15 2006, 4:00 pm – Inst: Eslami 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. AP Physics C Students I hope this set of questions are easier for everyone to turn in. Make sure that you bring the problem to me, if you do not know how to solve it, or you have tried it twice and you do not get it right. Good luck! 001 (part 1 of 2) 10 points The rectangular and polar coordinates of a point are ( x, y ) and ( r, θ ), where x = 5 and θ = 35 . Determine the value of r. Correct answer: 6 . 10387 . Explanation: The relation between rectangular and polar coordinates is: x = r cos θ y = r sin θ solving for r, r = x cos θ = 5 cos(35 ) = 6 . 10387 002 (part 2 of 2) 10 points Determine the value of y. Correct answer: 3 . 50104 . Explanation: y = r sin θ = (6 . 10387) sin(35 ) = 3 . 50104 keywords: 003 (part 1 of 2) 10 points Consider two vectors ~ A and ~ B and their re- sultant ~ A + ~ B . The magnitudes of the vectors ~ A and ~ B are, respectively, 18 . 7 and 5 . 3 and they act at 30 to each other. A B A + B Use the law of cosines to calculate the mag- nitude of the resultant vector ~ A + ~ B . Correct answer: 23 . 4402 . Explanation: a b c α β γ Law of cosines: c 2 = a 2 + b 2 - 2 a b cos γ For this problem, a = k ~ A k , b = k ~ B k , c = k ~ A + B k , δ is the angle between A and B , so that γ = 180 - δ , and β is the angle between A + B and A . c = p a 2 + b 2 - 2 a b cos γ 004 (part 2 of 2) 10 points Now use the law of sines to calculate the angle between the direction of the resultant vector A + B and the direction of the vector A .
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