Chapter 3 ProblemsChapter 3 Problems1, 2, 3 = straightforward, intermediate, challenging = full solution available in Student Solutions Manual/Study Guide = co ached solution with hints available at www.cp7e.com = biomedical applicationSection 3.1 Vectors and Their Properties 1. A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0° above the horizontal. Next, it travels 135 ft at an angle of 40.0° below the horizontal. Use graphical techniques to findthe roller coaster’s displacement from its starting point to the end of this movement. 2. An airplane flies 200 km due west from city A to city B and then 300 km in thedirection of 30.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? (b) Relative to city A, in what direction is city C? 3. A man lost in a maze makes three consecutive displacements so that at the end of his travel he is right back where he started. The first displacement is 8.00 m westward, and the second is 13.0 m northward. Use the graphical method to find the magnitude and direction of the third displacement. 4. A jogger runs 100 m due west, then changes direction for the second leg of the run. At the end of the run, she is 175 m away from the starting point at an angle of 15.0° north of west. What were the directionand length of her second displacement? Usegraphical techniques. 5. 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, the plane flies to lake B, which is 190 km and 30.0° west of north from lake A.Graphically determine the distance and direction from lake B to the base camp. 6. 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. 7. Vector A is 3.00 units in length and points along the positive x-axis. Vector B is4.00 units in length and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the vectors (a) A + B and (b) A – B. 8. Each of the displacement vectors A and B shown in Figure P3.8 has a magnitude of 3.00 m. Graphically find (a)A + B, (b) A – B, (c) B – A, and (d)A – 2B.Figure P3.8Section 3.2 Components of a Vector 9. A golfer takes two putts to get his ball into the hole once he is on the green. The first putt displaces the ball 6.00 m east, the second 5.40 m south. What displacement would have been needed to get the ball into the hole on the first putt? 10. A person walks 25.0° north of east for 3.10 km. How far would the person walk due north and due east to arrive at thesame location? 11. A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels? 12. While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 250 m east, 125 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance. 13. A vector has an x-component of –25.0 units and a y-component of 40.0 units.Find the magnitude and direction of the vector. 14. A quarterback takes the ball from theline of scrimmage, runs backwards for 10.0 yards, then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant displacement? 15. The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 41.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and itsspeed slows to 25.0 km/h. How far from Grand Bahama is the hurricane 4.50 h after it passes over the island? 16. A small map shows Atlanta to be 730miles in a direction 5° north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21° west of north from Atlanta. Assume a flat Earth, and use the given information to find the displacement from Dallas to Chicago. 17. A commuter airplane starts from an airport and takes the route shown in Figure P3.17. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west ofnorth, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point. Figure P3.1718. The helicopter view in Figure P3.18 shows two people pulling on a stubborn mule. Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of newtons (N). Figure P3.1819. A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120° with thepositive x-axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0° to the positive x-axis. Find the magnitude and direction of the second displacement. 20. An airplane starting from airport A flies 300 km east, then 350 km at 30.0° west of north, and then 150 km north to arrive finally at airport B. (a) The next day, anotherplane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight? (b) How far will the pilot travel in the flight? Assume there is no wind during either flight. 21. Long John Silver, a pirate, has buried his treasure on an island with five trees located at the following points: A (30.0 m,–20.0 m), B (60.0 m, 80.0 m), C (–10.0 m, –10.0 m), D (40.0 m, –30.0 m), and E (–70.0 m, 60.0 m). All of the points are measured relative to some origin, as in Figure P3.21. Long John’s map instructs you to start at A and move toward B, but cover only one-halfthe distance between A and B. Then move toward C, covering one-third the distance between your current location and C. Then move toward D, covering one-fourth the distance between where you are and D. Finally, move toward E, covering one-fifth