Farmer wants to Fence off his Four-Sided Plot with missing Side| Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.22

A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, and then correctly calculates the length and orientation of the fourth side D. What is his result?

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Flying in a Straight Line with Rotated Axes| Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.21

You fly 32.0 km in a straight line in still air in the direction 35.0° south of west.
(a) Find the distances you would have to fly straight south and then straight west to arrive at the same point. (This determination is equivalent to finding the components of the displacement along the south and west directions.)
(b) Find the distances you would have to fly first in a direction 45.0º south of west and then in a direction 45.0
° west of north. These are the components of the displacement along a different set of axes—one rotated 45.0°

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Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.18

You drive 7.50 km in a straight line in a direction 15° east of north.
(a) Find the distances you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east and north directions.)
(b) Show that you still arrive at the same point if the east and north legs are reversed in order.

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Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.17

Repeat Problem 3.16 using analytical techniques, but reverse the order of the two legs of the walk and show that you get the same final result. (This problem shows that adding them in reverse order gives the same result—that is, B+A=A+B) Discuss how taking another path to reach the same point might help to overcome an obstacle blocking your other path.

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Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.16

Solve the following problem using analytical techniques: 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 3.60, then this problem asks you to find their sum R = A + B .)

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Figure3.60 The two displacements A and B add to give a total displacement R having magnitude R and direction θ.

Note that you can also solve this graphically. Discuss why the analytical technique for solving this problem is potentially more accurate than the graphical technique.

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Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.14

Find the following for path D in Figure 3.58:
(a) the total distance traveled and
(b) the magnitude and direction of the displacement from start to finish.
In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.

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Figure 3.58 The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side.

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Vector Addition and Subtraction| Analytical Method| College Physics| Problem 3.13

Find the following for path C in Figure 3.58:
(a) the total distance traveled and
(b) the magnitude and direction of the displacement from start to finish.
In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.

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Figure 3.58 The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side.

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Vector Addition and Subtraction|College Physics| Problem 3.5

Suppose you first walk 12.0 m in a direction 20º west of north and then 20.0 m in a direction 40.0º 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 .)

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