HW 24 - Morby Grant Homework 24 Due noon Inst Drummond This...

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Morby, Grant – Homework 24 – Due: Mar 31 2006, noon – Inst: Drummond 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 3) 10 points Consider the two vectors ~ M = ( a, b ) = a ˆ ı + b ˆ and ~ N = ( c, d ) = c ˆ ı + d ˆ where, a and c represent the x -displacement and b and d represent the y -displacement in a Cartesian xy co-ordinate system. Note: ˆ ı and ˆ represent unit vectors ( i.e. vectors of length 1) in the x and y directions, respectively. What is the magnitude of the vector prod- uct k ~ M × ~ M k ? 1. k ~ M × ~ M k = 2 a b 2. k ~ M × ~ M k = a 2 - b 2 3. k ~ M × ~ M k = a + b 4. k ~ M × ~ M k = a 2 + 2 a b + b 2 5. k ~ M × ~ M k = - a b 6. k ~ M × ~ M k = p a 2 + b 2 7. k ~ M × ~ M k = 0 8. k ~ M × ~ M k = a b 9. k ~ M × ~ M k = a 2 - 2 a b + b 2 10. k ~ M × ~ M k = a 2 + b 2 002 (part 2 of 3) 10 points What is the magnitude of the vector product k ~ M × ~ N k ? 1. k ~ M × ~ N k = a 2 + b 2 + c 2 + d 2 2. k ~ M × ~ N k = a b - c d 3. k ~ M × ~ N k = a c + b d 4. k ~ M × ~ N k = a - b 5. k ~ M × ~ N k = a b c d 6. k ~ M × ~ N k = 0 7. k ~ M × ~ N k = a b + c d 8. k ~ M × ~ N k = a d - b c 9. k ~ M × ~ N k = a d + b c 10. k ~ M × ~ N k = a c - b d 003 (part 3 of 3) 10 points What is the direction of the vector product ~ M × ~ N ? 1. along the z -axis 2. along the x -axis 3. in the yz plane, but not along y or z 4. in the xy plane, but not along x or y 5. along the y -axis 6. in the xz plane, but not along x or z 7. none of these since its direction cannot be determined 004 (part 1 of 1) 10 points A satellite of mass 3 m moves on a plane in a circular orbit of radius r 3 m i about a spherical planet of mass M and radius R . The magni- tude of the velocity is v 3 m i . M is much larger than 3 m , so the center of mass of the system can be regarded as being located at the center of M which is at the origin of our coordinate system.
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