HW 01-solutions

# HW 01-solutions - cooper(mlc4285 HW 01 florin(55245 This...

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cooper (mlc4285) – HW 01 – florin – (55245) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Which of the following are vectors? List all that apply, separated by commas. A 4 . 5 B 0 C ( 0 . 7 , 0 . 7 , 0 . 5 ) D ( 0 , 2 . 3 , 1 ) E 1 × 10 6 F 6 · ( 14 , 0 , 22 ) Correct answer: C, D, F. Explanation: Options A , B , and E are scalar quanti- ties, so those choices are incorrect. Options C and D are clearly vectors, so they are cor- rect choices. The only option that might be somewhat tricky is F , which gives a vector be- ing multiplied by a scalar. But the product of such scalar multiplication is a new vector, so this choice is also correct. 002(part1of3)10.0points The figure shows the three dimensional vector vector d . What are the components of the vector d 1. (− 6 , 3 , 2 ) m 2. (− 6 , 3 , 2 ) m 3. (− 6 , 3 , 2 ) m correct 4. (− 6 , 3 , 2 ) m 5. ( 6 , 3 , 2 ) m Explanation: Since the tail of the vector is at the origin, the components of vector d can be read off from the figure being careful to get the sign correct. The x-component is 6 m; the y-component is +2 m; and the z-component is +3 m. 003(part2of3)10.0points If the tail of vector vector d is moved to location ( 3 . 2 , 3 . 2 , 3 . 5 ) m, where would the tip of the vector be located? 1. (− 2 . 8 , 6 . 2 , 5 . 5 ) m correct 2. ( 9 . 2 , 0 . 2 , 1 . 5 ) m 3. ( 3 . 2 , 3 . 2 , 3 . 5 ) m 4. (− 6 , 3 , 2 ) m 5. (− 6 , 3 , 2 ) m Explanation: Shifting the tail of the vector to ( 3 . 2 , 3 . 2 , 3 . 5 ) m means each component of the tip of the vector will be changed by the same amount as each component of the tail was changed. Thus, the tip will be at (− 6 + 3 . 2 , 3 + 3 . 2 , 2 + 3 . 5 ) m = (− 2 . 8 , 6 . 2 , 5 . 5 ) m. 004(part3of3)10.0points What is the length of the vector vectore = vector d ? Give your answer in units of meters. Correct answer: 7 m. Explanation: We use the Pythagorean theorem: | vectore | = radicalBig e 2 x + e 2 y + e 2 z = radicalBig (6 m) 2 + ( 3 m) 2 + ( 2 m) 2 = 49 m 2 = 7 . 0 m .

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cooper (mlc4285) – HW 01 – florin – (55245) 2 005(part1of2)10.0points Consider two vectors where F 1 = 97 N , F 2 = 74 N , θ 1 = 134 , and θ 2 = 43 , measured from the positive x axis with the counter-clockwise angular direction as positive.
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