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Math 160 Notes Packet #23 Vectors 2
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Suppose a car is heading NE (northeast) at 60 mph. We can use a vector to help draw a picture (see right). 3
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Suppose a car is heading NE (northeast) at 60 mph. We can use a vector to help draw a picture (see right). 4
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A vector consists of two parts: 1. a magnitude (ex: 60 mph) 2.a direction (ex: NE) By contrast, a scalar only has a magnitude (ex: 60 mph). 5
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A vector consists of two parts: 1. a magnitude (ex: 60 mph) 2.a direction (ex: NE) By contrast, a scalar only has a magnitude (ex: 60 mph). 6
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Examples of vectors include: displacement, velocity, acceleration, and force. Examples of scalars include: distance, speed, time, and volume. 7
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Examples of vectors include: displacement, velocity, acceleration, and force. Examples of scalars include: distance, speed, time, and volume. 8
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A vector has an initial point and a terminal point. The magnitude is the length of the vector. 9
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Two vectors are equal if they have the same magnitude and direction. So, all of the vectors to the right are equal. 11
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To add two vectors visually, put them tip to tail and make a triangle. 12
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Or put them tail to tail and make a parallelogram. 13
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You can stretch and shrink vectors by multiplying by a scalar. Negative values make the vector go in the opposite direction. 15
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31 unit vectors
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32 unit vectors
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33 unit vectors
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34 unit vectors
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It is often useful to break a vector into its horizontal and vertical components. 44
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Ex 5. A woman launches a boat from one shore of a straight river and wants to land at the point directly on the opposite shore. If the speed of the boat (relative to the water) is 10 mi/h and the river is flowing east at the rate of 5 mi/h, in what direction should she head the boat in order to arrive at the desired landing point? 48
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Ex 6. A 600-pound calculus book is suspended from two ropes. Find the tension in each rope. (Note: Since the book is not moving, it said to be in static equilibrium, so the sum of all forces acting on it is zero.) 49
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Ex 6. A 600-pound calculus book is suspended from two ropes. Find the tension in each rope. (Note: Since the book is not moving, it said to be in static equilibrium, so the sum of all forces acting on it is zero.) 50
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Ex 6. A 600-pound calculus book is suspended from two ropes. Find the tension in each rope. (Note: Since the book is not moving, it said to be in static equilibrium, so the sum of all forces acting on it is zero.) 51
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Ex 6. A 600-pound calculus book is suspended from two ropes. Find the tension in each rope. (Note: Since the book is not moving, it said to be in static equilibrium, so the sum of all forces acting on it is zero.) 52
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