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Copyright © 2011 Pearson, Inc.
6.1 Day 1 Vectors in the Plane Goal: Apply the arithmetic of vectors.
Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Two-Dimensional Vectors Vector Operations Direction Angles Applications of Vectors … and why These topics are important in many real-world applications, such as calculating the effect of the wind on an airplane’s path.
Copyright © 2011 Pearson, Inc. One vs. Two Quantities Magnitude (Size) temperature distance Speed mass Magnitude & Direction force velocity weight Slide
Copyright © 2011 Pearson, Inc. Vector - magnitude: direction: Slide
Copyright © 2011 Pearson, Inc. Vocabulary Component Form: Components: Standard representation: Zero vector: Slide
Copyright © 2011 Pearson, Inc. Slide Initial Point, Terminal Point, Equivalent
Copyright © 2011 Pearson, Inc. Slide Head Minus Tail (HMT) Rule
Copyright © 2011 Pearson, Inc. Example 1: Showing Vectors are Equivalent Show that the arrow from R = (-4, 2) to S = (-1, 6) is equivalent to the arrow from P = (2, -1) to Q = (5, 3). Slide
Copyright © 2011 Pearson, Inc. Slide Magnitude
Copyright © 2011 Pearson, Inc. Slide Example 2: Finding Magnitude of a Vector
Copyright © 2011 Pearson, Inc. Slide Vector Addition
Copyright © 2011 Pearson, Inc. Slide Vector Addition
Copyright © 2011 Pearson, Inc. Example 3: Performing Vector Addition Slide
Copyright © 2011 Pearson, Inc. Parallelogram Representation Slide
Copyright © 2011 Pearson, Inc. Scalar Multiplication scalar: Slide
Copyright © 2011 Pearson, Inc. Example 3: Performing Vector Operations Slide
Copyright © 2011 Pearson, Inc. Slide Exit Ticket Performing Vector Operations
Copyright © 2011 Pearson, Inc. 6.1 Day 2 Vectors in the Plane Goal: Use vectors to solve real-world problems.
Copyright © 2011 Pearson, Inc. Slide Resolving the Vector-
Copyright © 2011 Pearson, Inc. Example 5a: Finding the Components of a Vector Find the components of the vector v with direction angle 115 ˚ and magnitude 6. Slide
Copyright © 2011 Pearson, Inc. Example 5b: Finding the Components of a Vector Find the exact components of the vector v with direction angle 30 ˚ and magnitude 8. Slide
Copyright © 2011 Pearson, Inc. Example 5c: Finding the Components of a Vector Draw the indicated vector and show the components into which it is resolved. A cannonball is launched with a speed of 170 m/s at 40° above the horizontal. Slide
Copyright © 2011 Pearson, Inc. Velocity and Speed The velocity of a moving object is a vector because velocity has both magnitude and direction. The magnitude of velocity is ________. ________________ - the angle that a line of travel makes with due north, measured clockwise Slide
Copyright © 2011 Pearson, Inc. Example 7: Writing Velocity as a Vector A DC-10 jet aircraft is flying on a bearing of 65 ˚ at 500 mph. Find the component form of the velocity of the airplane. Recall that the bearing is the angle that the line of travel makes with due north, measured clockwise. Slide
Copyright © 2011 Pearson, Inc. Calculate Magnitude and Direction. Calculate the magnitude and direction of the vector. Slide
Copyright © 2011 Pearson, Inc. Example: Find the magnitude and direction angle of each vector. Slide
Copyright © 2011 Pearson, Inc. Summary Slide
Copyright © 2011 Pearson, Inc. 6.1 Day 3 Vectors in the Plane Goal: Calculate the resultant vector.
Copyright © 2011 Pearson, Inc. Resultant Vector Slide
Copyright © 2011 Pearson, Inc. Example: Add the Vectors to find the Resultant Vector Slide
Copyright © 2011 Pearson, Inc. Example: Calculating the Effect of Wind Velocity A jet carrying Dora the Explorer is flying at 400 mph on a course with a bearing of 30º. If the jet experiences a crosswind blowing due south at 20 mph, find the resultant speed and direction of the jet. Round all values throughout the problem and the final answer to the nearest tenth. Slide
Copyright © 2011 Pearson, Inc. Slide : Combining Forces
Copyright © 2011 Pearson, Inc. Solution Slide
10.2 Vectors and Vector Value Functions. Quantities that we measure that have magnitude but not direction are called scalars. Quantities such as force,
VECTORS IN A PLANE Pre-Calculus Section 6.3. CA content standards: Trigonometry 12.0 Students use trigonometry to determine unknown sides or angles in.
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6.3 Vectors in the plane Day 1 Objectives: - define vectors - identify component form of a vector - calculate the magnitude of a vector Warm Up Find the.
© 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their.
Lecture PowerPoints Chapter 3 Physics: Principles with Applications, 6 th edition Giancoli.
1/16/ : Vectors in Geometry Expectation: L1.2.3: Use vectors to represent quantities that have magnitude and direction, interpret direction and.
A two-dimensional vector v is determined by two points in the plane: an initial point P (also called the “tail” or basepoint) and a terminal point Q (also.
Do Now Period Homework Answers 1. t = 1.10 s, vf = 10.8 m/s 2. t = 5.10 s, d = m 3. vf = 5,772 m/s 4. d = 19.6 m, vf = 19.6.
Section Many of the quantities you work with in mathematics, such as those representing area, volume, and money in a bank account, are measures,
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P H Y S I C S Chapter 2: Two-Dimensional Motion Section 2A: Adding and Resolving Vectors Objectives: 1)We differentiate a scalar and vector 2)We will add.
2.1a Mechanics Forces in equilibrium Breithaupt pages 90 to 109 January 17 th 2011.
Vectors and Two-Dimensional Motion Vectors and Two-Dimensional Motion.
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AIR NAVIGATION Part 2 The Triangle of Velocities.
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Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 3 Two-Dimensional Motion and Vectors.
Kinematics The branch of mechanics that studies the motion of a body without caring about what caused the motion.
Year 10 Pathway C Mr. D. Patterson. Distinguish between scalar and vector quantities Add and subtract vectors in 2 dimensions using scaled diagrams.
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Solving 2-D Vectors Graphically Physics. Why? O You can and people have accurately represented a situation by drawing vectors to scale in order to recreate.
Vectors in the plane Vector operations. Vectors A vector is a quantity with both a magnitude and a direction. Vectors are used to represent velocity,
© Boardworks Ltd of 27 These icons indicate that teachers notes or useful web addresses are available in the Notes Page. This icon indicates the.
Please grab the copies for AP from the desk to the right of the door. Also, turn in your signature page to the plastic bin before the bell rings. AP Physics.
Vector Multiplication: The Cross Product. When two vectors are “multiplied” to form a 3 rd vector, the new vector is called the cross product of the original.
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