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# Applied Math 40S Slides April 25, 2007

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More applications of vectors and pretest problems.

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### Applied Math 40S Slides April 25, 2007

1. 1. The vector represents a velocity of 50 km/h towards [030°]. What is ? (a) 50 km/h towards [-120°] (b) 50 km/h towards [120°] (c) 200 km/h towards [030°] (d) 200 km/h towards [120°]
2. 2. The airspeed of an airplane is 300 km/h. A wind blows from due east at 50 km/h. In what direction does the plane need to head in order to travel due north? (a) [010°] (b) [296°] (c) [304°] (d) [350°]
3. 3. Corrie and Allan are pulling on a rock with equal force, they are at an angle of 40° to each other. If the resultant vector has a force of 50 newtons, determine the magnitude of the force with which each is pulling.
4. 4. Corrie and Allan are pulling on a rock with equal force, they are at an angle of 40° to each other. If the resultant force remains at 50 newtons, at what angle could Corrie and Allan pull in order for Corrie to pull with double the force of Allan?
5. 5. An airplane travels at a speed of 250 km/h in a direction 30° north of west for one hour. It then travels at a speed of 300 km/h for 40 minutes in a direction of 42° east of north. To return directly to its starting point, in what direction and what distance must the airplane travel? Show all work.
6. 6. Gretta’s Desert Adventure! Gretta is competing in an orienteering contest that takes place in an open desert region at night. The contest consists of riding her dune buggy for the first three parts (legs), and then walking back to the starting point. Her navigational equipment consists of the odometer on the dune buggy and a handheld compass. She also carries a flashlight (with spare batteries) so that she can read her compass and walk in the dark. Her directions are as follows: 1. The first leg is 7.5 km on a bearing of 70°. 2. The second leg is 12 km on a bearing of 190°. 3. The third leg is 10 km on a bearing of 310°. 4. The fourth and final leg is walking back to the starting point. In what direction must she walk, and how far must she walk, to complete the fourth leg of the contest? Round both answers to the nearest tenth.
7. 7. 1. The first leg is 7.5 km on a bearing of 70°. 2. The second leg is 12 km on a bearing of 190°. 3. The third leg is 10 km on a bearing of 310°. 4. The fourth and final leg is walking back to the starting point.
8. 8. 1. The first leg is 7.5 km on a bearing of 70°. 2. The second leg is 12 km on a bearing of 190°. 3. The third leg is 10 km on a bearing of 310°. 4. The fourth and final leg is walking back to the starting point. We use the program TRISOLVE2 on our graphing calculators to get the purple values.
9. 9. 1. The first leg is 7.5 km on a bearing of 70°. 2. The second leg is 12 km on a bearing of 190°. 3. The third leg is 10 km on a bearing of 310°. 4. The fourth and final leg is walking back to the starting point. In what direction must she walk, and how far must she walk, to complete the fourth leg of the contest? Round both answers to the nearest tenth. We use the program TRISOLVE2 on our graphing calculators to get the black values.
10. 10. Topo G. sails his boat 9 km at 300°, then 12 km at 200°, and finally 18 km at 115°. He thinks he should be close to his starting point, which is his home. Determine his displacement from his home. Can he get back home in one hour if his sailing speed is 12 km/h? Use this problem, and the next three slides, as extra practice to study for tomorrow's test.
11. 11. Two forces, 120lb and 200lb, act on a body and make a 52 degree angle with each other. What's the magnitude of the resultant of the force and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force?
12. 12. Busy Bees ... A worker bee is ready to fly out and gather pollen, but on her way out of the hive she meets one of her fellow workers who is just returning. The incoming bee tells her, in bee-dance language, that there is a good pollen source 0.3 km southeast of the hive. However, before the outgoing bee leaves the hive, she meets another incoming bee and she tells her that there is also a pollen source 0.5 km due south of the hive. If the busy worker is to visit both of these pollen sources in their respective order before returning to the hive, what direction and distance will she need to fly to get from the first source to the second source? If her average velocity is about 1.5 m/s, how long will it take her to get from the first to the second source?
13. 13. A butterfly is flying in a garden. First it travels due south for 6.0 m and then 37 W of N for 10 m. Assuming that the positive x-direction is east, and the positive y-direction is north, (a) what are the coordinates of the butterfly's final position relative to its initial position? (b) what are the magnitude and direction of the displacement of the butterfly (relative to its initial position)?