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# HW #3 - homework 03 FONTENOT BRIAN Due Feb 4 2008 4:00 am...

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homework 03 – FONTENOT, BRIAN – Due: Feb 4 2008, 4:00 am 1 Question 1, chap 3, sect 4. part 1 of 3 10 points Consider the two vectors vector M = ( a, b ) = a ˆ ı + b ˆ and vector N = ( c, d ) = c ˆ ı + d ˆ , where a = 4, b = 4, c = 3, and d = - 3. 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 vector M × vector M ? Question 2, chap 3, sect 4. part 2 of 3 10 points What is the magnitude of the vector prod- uct vector M × vector N ? Question 3, chap 3, sect 4. part 3 of 3 10 points What is the direction of the vector product vector M × vector N ? 1. none of these since its direction cannot be determined 2. in the xz plane, but not along x or z 3. along the y -axis 4. in the xy plane, but not along x or y 5. along the z -axis 6. along the x -axis 7. in the yz plane, but not along y or z Question 4, chap 3, sect 4. part 1 of 2 10 points Vector vector A is 0 . 857 units long and points in the positive y direction. Vector vector B has a negative x component 4 . 35 units long, a positive y component 4 . 43 units long, and no z component. Find vector A · vector B . Answer in units of units 2 . Question 5, chap 3, sect 4. part 2 of 2 10 points What is the angle between vector A and vector B ? Answer in units of . Question 6, chap 4, sect 1. part 1 of 1 10 points Suppose that three balls are rolled simulta- neously from the top of a hill along the slopes as shown below. 1 2 3 Which one reaches the bottom first? 1. 2 2. 1 and 2 3. 1 and 3 4. 1 5. 3 6. 2 and 3 7. The balls reach the bottom at the same time. Question 7, chap 4, sect 1. part 1 of 1 10 points A ball rolling up a hill has vector velocities vectorv 1 and vectorv 2 at times t 1 and t 2 , respectively, as shown in the figure. v 1 initial v 2 final Which vector diagram below most accu-

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homework 03 – FONTENOT, BRIAN – Due: Feb 4 2008, 4:00 am 2 rately depicts the direction of the ball’s aver- age acceleration over the interval? 1. 2. 3. 4. Zero vector. 5. 6. 7. 8. 9. Question 8, chap 4, sect 2. part 1 of 1 10 points Consider the instantaneous velocity of a body. This velocity is always in the direction of 1. the least resistance at that instant.
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