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Transcript

Chapter 3 | Two-Dimensional Kinematics Problems & Exercises 3.2 Vector Addition and Subtraction: Graphical Methods Use graphical methods to solve these problems. You may assume data taken from graphs is accurate to three digits. 1. Find the following for path A in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish. Figure 3.56 6. Repeat the problem above, but reverse the order of the two legs of the walk; show that you get the same final result. That is, you first walk leg B , which is 20.0 m in a direction exactly 40Âº south of west, and then leg A , which is 12.0 m in a 20Âº west of north. (This problem shows that A + B = B + A .) direction exactly Figure 3.54 The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side. 2. Find the following for path B in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish. 3. Find the north and east components of the displacement for the hikers shown in Figure 3.52. 4. Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.55, then this problem asks you to find their sum R = A + B .) 7. (a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0Âº north of east (which is equivalent to subtracting B from A âthat is, to finding Râ² = A â B ). (b) Repeat the problem two problems 40.0Âº south of west and then 12.0 m in a direction 20.0Âº east of south (which is equivalent to subtracting A from B âthat is, to finding Râ²â² = B - A = - Râ² ). Show that this is the case. prior, but now you first walk 20.0 m in a direction 8. Show that the order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors A , B , and C , all having different lengths and directions. Find the sum A + B + C then find their sum when added in a different order and show the result is the same. (There are five other orders in which A , B , and C can be added; choose only one.) 9. Show that the sum of the vectors discussed in Example 3.2 gives the result shown in Figure 3.24. 10. Find the magnitudes of velocities v A and v B in Figure 3.57 Figure 3.55 The two displacements displacement R having magnitude A R and B add to give a total and direction 5. Suppose you first walk 12.0 m in a direction Î¸. 20Âº west of north and then 20.0 m in a direction 40.0Âº south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this problem finds their sum R = A + B .) Figure 3.57 The two velocities vA 11. Find the components of and vB add to give a total v tot . v tot along the x- and y-axes in Figure 3.57. 18