14_2dvectors - Lesson 14: Vectors in Two Dimensions Two...

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Lesson 14: Vectors in Two Dimensions Two dimensional problems are a little tougher, because we are no longer just lining up collinear vectors and doing quick math. Instead, we need to pay attention to how the vectors form a more complex (but not very complex) diagram. The majority of these diagrams will involve right angle triangles. If they are right angle triangles, just use your regular trig (SOH CAH TOA) and pythagoras (c 2 = a 2 + b 2 ). You'll want to be thinking about physics as you set up your diagram (so that you get everything pointing head-to-tail and stuff) and then switch over to doing math just like any trig problem. Components of Vectors One of the most important ideas in vectors is components. Just like a component stereo system is made of several individual parts working together, components of vectors are the individual parts that add up to the overall resultant . Example 1 : A car drives 10km [E] and then 7 km [N] . Determine its displacement. First, draw a proper diagram: The red and the blue vectors are the components of the resultant. The red and blue components show you how walking East and the North will result in you moving more or less in a North-East direction. Notice how this diagram even shows the vectors being added in the correct order according to the question. 10 km [E] is shown leading up to 7.0 km [N] . Start at the tail of the red arrow and follow the path it takes you along. You eventually end up at the head of the blue vector. If you added them with 7.0 km [N] and then 10 km [E] you would still get the same final answer, just with a different angle because of a different reference point. The resultant is drawn in head-to-head and tail-to-tail, just like a resultant is always supposed to be. This is certainly a right angle triangle, so just use c
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This note was uploaded on 12/02/2011 for the course PHYSICS 235 taught by Professor Staff during the Fall '08 term at Rutgers.

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14_2dvectors - Lesson 14: Vectors in Two Dimensions Two...

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