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Unformatted text preview: Answer key for first exam version A 1 1. Vector ~ A = (5 . 7 ,- 3 . 6) and ~ B = (- 9 . 8 ,- 6 . 5). Then the difference ~ D = ~ B- ~ A = (- 15 . 5 ,- 2 . 9). So the magnitude D = q (- 15 . 5) 2 + (- 2 . 9) 2 = 15 . 8. Answer = C (16) 72% correctly answered 2. Rotating a vector changes its direction. One cannot add a scalar to a vector, although one can multiply a vector by a scaler. Only vectors of the same mag- nitude can be summed to zero (they would be anti-parallel). A vector with a non-zero component must have a magnitude of at least the size of that compo- nent. The magnitude of a vector is independent of the coordinate system used to describe the components of the vector. That is why having vectors in Physics is so useful, since Physics does not depend upon the choice of any (inertial only) coordinate system. Answer = A 69% answered correctly 3. The vector ~ A = (3 . 9 ,- 4 . 0). The angle of the vector is tan- 1 ( A x , A y ) = tan- 1 (3 . 9 ,- 4 . 0) =- 45 . 6 o = 314.3 o . Note that if the problem had specified ~ A = (- 3 . 9 , 4 . 0), and you divided first with your calculator, your calculator might have returned -45.6 o as well. However, the correct answer would have been in the second quadrant instead of the fourth quadrant. Answer = B (314) 80% answered correctly 4. The vector ~ A has a magnitude of 4.8 and is in the second quadrant, at an angle of 18 degrees with respect to the y axis. Its x and y components are ( A cos(18 + 90) , A sin(18 + 90)) = (- 1 . 48 , 4 . 57), where the 90 o is being added because the angle was specified with respect to the y axis instead of the x axis. Answer = C (-1.5, +4.6) 82% answered correctly 5. The net displacement ~ AC is- 5 meters, and this displacement is accomplished in 28 seconds. Thus the average velocity ~v AC = ~ AC/ 28 seconds = -0.179 m/s. The negative sign indicates that the direction of the average velocity is the negative x direction. Answer = A (-0.179 m/s) 74% answered correctly 6. The total distance traveled (from A to B to C) is 5 + 10 + 10 = 25 meters, in 28 seconds. So the average speed is 25 / 28 = 0 . 893 m/s....
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- Spring '08