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# chapter3.key - CHAPTER 3 VECTOR quantities Vectors have...

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CHAPTER 3 Two-Dimensional Motion and Vectors Representations: x y (x, y) (x, y) (r, ! ) VECTOR quantities: Vectors have magnitude and direction. Other vectors: velocity, acceleration, momentum, force … Vector Addition/Subtraction 2nd vector begins at end of first vector Order doesn’t matter Vector addition Vector subtraction A – B can be interpreted as A+(-B) Vector Components Cartesian components are projections along the x- and y-axes A x = A cos ! A y = A sin ! Going backwards, A = A x 2 + A y 2 and ! = tan " 1 A y A x Example 3.1a The magnitude of (A-B) is : a) <0 b) =0 c) >0 Example 3.1b The x-component of (A-B) is: a) <0 b) =0 c) >0

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Example 3.1c The y-component of (A-B) > 0 a) <0 b) =0 c) >0 Example 3.2 Alice and Bob carry a bottle of wine to a picnic site. Alice carries the bottle 5 miles due east, and Bob carries the bottle another 10 miles traveling 30 degrees north of east. Carol, who is bringing the glasses, takes a short cut and goes directly to the picnic site. How far did Carol walk? What was Carol’s direction? 14.55 miles, at 20.10 degrees Alice Bob Carol Arcsin, Arccos and Arctan: Watch out! same sine same cosine same tangent Arcsin, Arccos and Arctan functions can yield wrong angles if x or y are negative. 2-dim Motion: Velocity Graphically, v = " r / " t It is a vector (rate of change of position) Trajectory Multiplying/Dividing Vectors by Scalars, e.g. " r / " t Vector multiplied/divided by scalar is a vector Magnitude of new vector is magnitude of orginal vector multiplied/divided by |scalar| Direction of new vector same as original vector Principles of 2-d Motion X- and Y-motion are independent Two separate 1-d problems To get trajectory (y vs. x) 1.Solve for x(t) and y(t) 2.Invert one Eq. to get t(x) 3.Insert t(x) into y(t) to get y(x)
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chapter3.key - CHAPTER 3 VECTOR quantities Vectors have...

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