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**Unformatted text preview: **Chapter 3 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 3.1 Coordinate Systems 1. The polar coordinates of a point are r = 5.50 m and θ = 240°. What are the Cartesian coordinates of this point? 2. Two points in a plane have polar coordinates (2.50 m, 30.0°) and (3.80 m, 120.0°). Determine (a) the Cartesian coordinates of these points and (b) the distance between them. 3. A fly lands on one wall of a room. The lower left-hand corner of the wall is selected as the origin of a two-dimensional Cartesian coordinate system. If the fly is located at the point having coordinates (2.00, 1.00) m, (a) how far is it from the corner of the room? (b) What is its location in polar coordinates? 4. Two points in the xy plane have Cartesian coordinates (2.00, - 4.00) m and (- 3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates. 5. If the rectangular coordinates of a point are given by (2, y ) and its polar coordinates are ( r , 30 ° ), determine y and r . 6. If the polar coordinates of the point ( x, y ) are ( r, θ ), determine the polar coordinates for the points: (a) (- x, y ), (b) (- 2 x, - 2 y ), and (c) (3 x, - 3 y ). Section 3.2 Vector and Scalar Quantities Section 3.3 Some Properties of Vectors 7. A surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, she walks 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is 35.0 ° . How wide is the river? 8. A pedestrian moves 6.00 km east and then 13.0 km north. Find the magnitude and direction of the resultant displacement vector using the graphical method. 9. A plane flies from base camp to lake A, a distance of 280 km at a direction of 20.0 ° north of east. After dropping off supplies it flies to lake B , which is 190 km at 30.0 ° west of north from lake A. Graphically determine the distance and direction from lake B to the base camp. 10. Vector A has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x axis. Using graphical methods, find (a) the vector sum A + B and (b) the vector difference A - B ....

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