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HW #1-1-solutions

HW #1-1-solutions - pasha(sep635 HW#1-1 Antoniewicz(56445...

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pasha (sep635) – HW#1-1 – Antoniewicz – (56445) 1 This print-out should have 36 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 of 5) 2.0 points Consider vectors ~ A and ~ B such that ~ A = h 200 , - 200 , - 300 i and ~ B = h- 300 , 500 , 300 i . ±ind ~ A + ~ B . 1. h- 100 , 300 , 0 i correct 2. h- 100 , 200 , - 100 i 3. h 200 , 100 , - 200 i 4. h 300 , 0 , 100 i 5. h 200 , 300 , 200 i Explanation: To add vectors, we add respective compo- nents: A x + B x =200+( - 300) = - 100 , A y + B y = - 200 + 500 = 300 , and A z + B z = - 300 + 300 = 0 , so ~ A + ~ B = h A x + B x ,A y + B y z + B z i = h- 100 , 300 , 0 i . 002 (part 2 of 5) 2.0 points ±ind ± ± ± ~ A + ~ B ± ± ± . Correct answer: 316 . 228. Explanation: The magnitude oF ~ A + ~ B is ± ± ± ~ A + ~ B ± ± ± = q ( A x + B x ) 2 +( A y + B y ) 2 A z + B z ) 2 = q ( - 100) 2 +(300) 2 +(0) 2 =316 . 228 . 003 (part 3 of 5) 2.0 points ±ind ± ± ± ~ A ± ± ± . Correct answer: 412 . 311. Explanation: We Follow the same procedure as For the previous part oF the problem. ± ± ± ~ A ± ± ± = q A 2 x + A 2 y + A 2 z = q (200) 2 - 200) 2 - 300) 2 =412 . 311 . 004 (part 4 of 5) 2.0 points ±ind ± ± ± ~ B ± ± ± . Correct answer: 655 . 744. Explanation: We Follow the same procedure again. ± ± ± ~ B ± ± ± = q B 2 x + B 2 y + B 2 z = q ( - 300) 2 +(500) 2 2 =655 . 744 . 005 (part 5 of 5) 2.0 points ±ind ± ± ± ~ A ± ± ± + ± ± ± ~ B ± ± ± . Correct answer: 1068 . 05. Explanation: Here we simply add the values we obtained in parts 3 and 4: ± ± ± ~ A ± ± ± + ± ± ± ~ B ± ± ± . 311 + 655 . 744 =1068 . 05 . 006 10.0 points Consider the Following fgure:
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pasha (sep635) – HW#1-1 – Antoniewicz – (56445) 2 ~ t ~ r ~ s Which of the following statements about the three vectors in the Fgure are correct? List all that apply, separated by commas. A ~ s = ~ t - ~ r B ~ r = ~ t - ~ s C ~ r + ~ t = ~ s D ~ s + ~ t = ~ r E ~ r + ~ s = ~ t Correct answer: A, B, E. Explanation: Vector subtraction can be tricky. Just as one way to subtract scalar quantities is to add the negative of the number being subtracted ( i.e. ,in s t e ado f5 - 3=2w ec ou ldw r i t e 5+( - 3) = 2), we can do the same with vectors. We start by writing down the Frst vector. ±or option A ,theFrstvectorinthe subtraction is ~ t ,sowedrawit : ~ t Then, we add the negative of the vector being subtracted. When we write down - ~ r ,it will be pointing in the opposite direction from ~ r .W ep lace - ~ r ’s starting point at the tip of ~ t , and from here, we are simply adding vectors: ~ t ~ s - ~ r Notice that the resultant vector, ~ s ,i sex - actly the same as the original ~ s in the Fgure we started with. So ~ t +( - ~ r )= ~ t - ~ r = ~ s, and option A is true. ±ollowing the same procedure for the re- maining options, we can determine that A , B ,and E are true statements, while the oth- ers are false. 007 (part 1 of 3) 4.0 points Aunitvector ~ v lies in the xy plane, at an angle of 150 from the + x axis, with a positive y component. What are the components of the unit vector ˆ v = h ˆ v x , ˆ v y , ˆ v z i ? ~ v 150 ±ind ˆ v x . Correct answer: - 0 . 866025. Explanation: ~ v 150 sin 150 cos 150 The x component of ˆ v is given by ˆ v x =cos150 = - 0 . 866025 . 008 (part 2 of 3) 3.0 points ±ind ˆ v y .
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HW #1-1-solutions - pasha(sep635 HW#1-1 Antoniewicz(56445...

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