5 Displacement and Force in Two Dimensions BIGIDEA Write the Big Idea for this chapter.

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1 5 Displacement and Force in Two Dimensions BIGIDEA Write the Big Idea for this chapter. Use the What I Know column to list the things you know about the Big Idea. Then list the questions you have about the Big Idea in the What I Want to Find Out column. As you read the chapter, fill in the What I Learned column. K What I Know W What I Want to Find Out L What I Learned 71

2 5 Displacement and Force in Two Dimensions 1 Vectors MAINIDEA Write the Main Idea for this section. REVIEW VOCABULARY vector Recall and write the definition of the Review Vocabulary term. vector NEW VOCABULARY Use your book to fill in the term that matches each definition. projections of a vector parallel to the x-axis and to the y-axis process of breaking a vector into its components 72

3 Student Edition, pp Write two bullet points about vectors in two dimensions. GET IT? Describe the process of graphically adding vectors using a protractor and a ruler. Write the law of sines below, and explain when you should use it. Write the law of cosines below, and explain when you should use it. 73

4 Student Edition, pp Explain how vector components are related to vector resolution. GET IT? Explain how you should measure the direction of a vector. Identify whether the components of a vector will be positive or negative in each quadrant. Second quadrant 90 < θ < 180 Third quadrant 180 < θ < 270 +y First quadrant 0 < θ < 90 Fourth quadrant 270 < θ < 360 +x 74

5 Student Edition, p. 128 Use with Example Problem 2. Use this column for scratch work and sketches. TRY IT! Problem FINDING YOUR WAY HOME You are on a hike. Your camp is 13.0 km away, in the direction 45.0 north of east. You must walk due north to avoid walking through a bog. If you walk due north for 7.0 km, how far, and in what direction, would you have to walk to reach your camp? 1. ANALYZE AND SKETCH THE PROBLEM KNOWNS UNKNOWNS A = =? R = =? 2. SOLVE FOR THE UNKNOWN Determine the angle you should use for the components of R. Find the components of R. Because A is due north, A x = 0.0 km and A y = 7.0 km. Use the components of R and A to find the components of B. Use the components of vector B to find the magnitude of vector B. Locate the tail of vector B at the origin of a coordinate system, and draw the components B x and B y. The vector B is in the first quadrant. Use the tangent to find the direction of vector B. 75

6 Student Edition, pp. 128 TRY IT! (continued) 3. EVALUATE THE ANSWER Are the units correct? Do the signs make sense? SUMMARIZE How does the MAINIDEA for this section relate to the chapter s BIGIDEA? REVIEW IT! 11. MAINIDEA Find the components of vector M, shown in Figure Components of Vectors Find the components of vectors K and L in Figure Vector Sum Find the sum of the three vectors shown in Figure 9. Figure Vector Difference Subtract vector K from vector L, shown in Figure 9. K L M

7 15. Commutative Operations Mathematicians say that vector addition is commutative because the order in which vectors are added does not matter. a. Use the vectors from Figure 9 to show graphically that M + L = L + M. b. Which ordinary arithmetic operations (addition, subtraction, multiplication, and division) are commutative? Which are not? Give an example of each operation to support your conclusion. 16. Distance v. Displacement Is the distance you walk equal to the magnitude of your displacement? Give an example that supports your conclusion. 17. Critical Thinking You move a box through one displacement and then through a second displacement. The magnitudes of the two displacements are unequal. Could the displacements have directions such that the resultant displacement is zero? Suppose you move the box through three displacements of unequal magnitude. Could the resultant displacement be zero? Support your conclusion with a diagram. 77