Honors Precalculus 4/24/18 IDs on and showing.

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Presentation transcript:

Honors Precalculus 4/24/18 IDs on and showing. Check-in Direction Angle and Components. Questions on Direction Angles and Components. Complete Combinations of Vectors and Resultant Vectors.

Section 6.1 Combination of Vectors Resultant Vectors Honors PreCalculus Section 6.1 Combination of Vectors Resultant Vectors

Example 1: A boat is traveling due West at a speed of 20 mph. There is an 8 mph current flowing at a bearing of 60º. What is the “true” speed of the boat? N Step 1: Resolve each vector into its components 60º 8mph 20 mph

Example 1: A boat is traveling due West at a speed of 20 mph. There is an 8 mph current flowing at a bearing of 60º. What is the “true” speed of the boat? N Step 2: Add horizontal components; Add vertical components. In other words; add the vectors 8mph 20 mph So, the boat’s “true” speed due West is 13.07 mph. Without compensating for the current (by steering into it), it’s traveling 4 mph North.

Example 1: A boat is traveling due West at a speed of 20 mph. There is an 8 mph current flowing at a bearing of 60º. What is the “true” speed of the boat? N The resultant vector shows the actual direction of the boat, without compensating for the current

Example 2: An airplane is flying 350 mph at a bearing of 132º. If the wind is blowing 47 mph at a bearing of 300º, find: the actual (“ground”) speed of the plane and the bearing of the plane as a result of the wind N 150º 47 132º 318º 300º 350

Example 2: An airplane is flying 350 mph at a bearing of 132º. If the wind is blowing 47 mph at a bearing of 300º, find: the actual (“ground”) speed of the plane and the bearing of the plane as a result of the wind N 150º 47 318º 350

Example 2: An airplane is flying 350 mph at a bearing of 132º. If the wind is blowing 47 mph at a bearing of 300º, find: the actual (“ground”) speed of the plane and the bearing of the plane as a result of the wind N a) “ground” speed of the plane is the magnitude of the resultant vector b) Direction angle of resultant vector Bearing:

Example 3: Three forces all work on the same object. Force 1 = 100 lb at an angle of 50º Force 2 = 50 lb at an angle of 160º Force 3 = 80 lb at an angle of -20º Find the resultant force, and the angle at which it acts. N 100 160º 50º 50 -20º 80