868 CHAPTER 8 Applications of Trigonometry Use the given vectors to sketch each of the following. 35. a - b 36. a + 3c Given two forces and the angle between them, find the magnitude of the resultant force. 37. 528 130 lb 100 lb Vector v has the given magnitude and direction angle. Find the horizontal and vertical components of v. 39. v = 964, u = 154° 20′ 40. v = 50, u = 45° (Give exact values.) Find the magnitude and direction angle for u rounded to the nearest tenth. 41. u = 8-9, 129 42. u = 821, -209 43. Let v = 2i - j and u = -3i + 2j. Express each in terms of i and j. (a) 2v + u (b) 2v (c) v - 3u Find the angle between the vectors. Round to the nearest tenth of a degree. If the vectors are orthogonal, say so. 44. 83, -29, 8-1, 39 45. 85, -39, 83, 59 46. 80, 49, 8-4, 49 Solve each problem. 47. Weight of a Sled and Passenger Paula and Steve are pulling their daughter Jessie on a sled. Steve pulls with a force of 18 lb at an angle of 10°. Paula pulls with a force of 12 lb at an angle of 15°. Find the magnitude of the resultant force on Jessie and the sled. 158 108 12 lb 18 lb Sled 48. Force Placed on a Barge One boat pulls a barge with a force of 100 newtons. Another boat pulls the barge at an angle of 45° to the first force, with a force of 200 newtons. Find the resultant force acting on the barge, to the nearest unit, and the angle between the resultant and the first boat, to the nearest tenth. 49. Direction and Speed of a Plane A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310°. A wind of 37 mph is blowing from a bearing of 212°. In what direction should the pilot fly, and what will be her ground speed? 50. Angle of a Hill A 186-lb force is required to hold a 2800-lb car on a hill. What angle does the hill make with the horizontal? 51. Incline Force Find the force required to keep a 75-lb sled from sliding down an incline that makes an angle of 27° with the horizontal. (Assume there is no friction.) 52. Speed and Direction of a Boat A boat travels 15 km per hr in still water. The boat is traveling across a large river, on a bearing of 130°. The current in the river, coming from the west, has a speed of 7 km per hr. Find the resulting speed of the boat and its resulting direction of travel. a b c 38. forces of 142 and 215 newtons, forming an angle of 112°
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