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In this unit, we explore vector modeling through various practical examples. First, we evaluate the forces exerted by two tugboats towing a barge, calculating the magnitude of the equilibrant when pulling at different strengths and an angle of 32 degrees. Next, we analyze two forces acting on a point, determining the angle between them when their combined effect equals a known resultant force. Finally, we assess a sailboat navigating east with a water current moving south, calculating its resultant velocity in terms of distance and bearing.
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5.4 Vectors (Part 4)Unit 1 OBJ: SWBAT: Model with Vectors HW: 5.4 Modeling with Vectors Part 4
Example 1: • Two tugboats are towing a barge. The first tugboat pulls with a force of 3 tons. The second tugboat pulls with a force of 3.5 tons. If the angle between the tow lines is 32o, find the magnitude of the equilibrant. 148o 3.5 tons 3 tons 32o 3.5 tons 3 tons
Example 2: • Two forces of 5.4 N and 6.2 N act on a point. The resultant of the two forces is a force of 9.3 N. Find the angle between the 5.4 N and 6.2 N forces. 6.2 N 5.4 N 9.3 N 6.2 N 5.4 N
Example 3: • A sailboat is headed east at 18 mph relative to the water. A current is moving the water south at 3 mph. Find the resultant vector as a distance and a bearing. 18 mph 3 mph
