809 8.3 Geometrically Defined Vectors and Applications 40. Force Needed for a Monolith If the causeway in Exercise 39 were 500 ft longer and the monolith weighed 10 tons more, how much force would be required? 41. Incline Angle A force of 18.0 lb is required to hold a 60.0-lb stump grinder on an incline. What angle does the incline make with the horizontal? 42. Incline Angle A force of 30.0 lb is required to hold an 80.0-lb pressure washer on an incline. What angle does the incline make with the horizontal? 43. Weight of a Box Two people are carrying a box. One person exerts a force of 150 lb at an angle of 62.4° with the horizontal. The other person exerts a force of 114 lb at an angle of 54.9°. Find the weight of the box. 44. Weight of a Crate and Tension of a Rope A crate is supported by two ropes. One rope makes an angle of 46° 20′ with the horizontal and has a tension of 89.6 lb on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope. 150 lb 114 lb 62.48 54.98 Box Solve each problem. See Examples 5 and 6. 45. Distance and Bearing of a Ship A ship leaves port on a bearing of 34.0° and travels 10.4 mi. The ship then turns due east and travels 4.6 mi. How far is the ship from port, and what is its bearing from port? 46. Distance and Bearing of a Luxury Liner A luxury liner leaves port on a bearing of 110.0° and travels 8.8 mi. It then turns due west and travels 2.4 mi. How far is the liner from port, and what is its bearing from port? 47. Distance of a Ship from Its Starting Point Starting at point A, a ship sails 18.5 km on a bearing of 189°, then turns and sails 47.8 km on a bearing of 317°. Find the distance of the ship from point A. 48. Distance of a Ship from Its Starting Point Starting at point X, a ship sails 15.5 km on a bearing of 200°, then turns and sails 2.4 km on a bearing of 320°. Find the distance of the ship from point X. 49. Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat. 50. Movement of a Motorboat Suppose we would like to cross a 132-ft-wide river in a motorboat. Assume that the motorboat can travel at 7.0 mph relative to the water and that the current is flowing west at the rate of 3.0 mph. The bearing u is chosen so that the motorboat will land at a point exactly across from the starting point. (a) At what speed will the motorboat be traveling relative to the banks? (b) How long will it take for the motorboat to make the crossing? (c) What is the measure of angle u? 3.0 7.0 Ending point Starting point u
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