chapter3 - CHAPTER 3 Two-Dimensional Motion and Vectors...

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CHAPTER 3 CHAPTER 3 Two-Dimensional Motion and Vectors
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Representations: Representations: x y (x, y) (x, y) (r, θ ) VECTOR quantities: VECTOR quantities: Vectors have magnitude and direction. Other vectors: velocity, acceleration, momentum, force …
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Vector Addition/Subtraction 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)
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Vector Components Vector Components Cartesian components are projections along the x- and y-axes A x = A cos q A y = A sin q Going backwards, A = +  θ=  -
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Example 3.1a Example 3.1a The magnitude of (A-B) is : a) <0 b) =0 c) >0
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Example 3.1b Example 3.1b The x-component of (A-B) is: a) <0 b) =0 c) >0
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Example 3.1c Example 3.1c The y-component of (A-B) > 0 a) <0 b) =0 c) >0
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Example 3.2 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 Carol
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Arcsin, Arccos and Arctan: Watch out! 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.
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2-dim Motion: Velocity 2-dim Motion: Velocity Graphically, v = r / t It is a vector (rate of change of position) Trajectory
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Multiplying/Dividing Vectors Multiplying/Dividing Vectors by Scalars, e.g.
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chapter3 - CHAPTER 3 Two-Dimensional Motion and Vectors...

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