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Bell Work: What is one way to determine the magnitude and direction when you are dealing with vectors?

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Objectives: TLW compare/contrast Vectors and Scalars. TLW Add & Subtract Vectors. TLW analyze Two-Dimensional Motion.

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Spi’s & Cle’s CLE 3231.1.4 Investigate kinematics and dynamics. CLE.3231.Math.4 Investigate trigonometric connections to physics 3231.Math.6 Solve for all variables based on a formula. 3231.Math.10 Utilize trigonometric functions (sine, cosine, and tangent) to solve simple vector problems. 3231.Math.11 Apply the laws of sine SPI.3231.1.2 Given various examples of quantities, categorize them as scalar or vector quantities.

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What is a Scalar? A quantity that has magnitude but not direction. Examples: Speed, Volume, Pages in a Book

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What is a Vector? A physical quantity that has both direction and magnitude. Examples: Displacement &Velocity

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Symbols: Scalars and Vectors Vector Quantities – Boldface V= 3.5m/s northeast (velocity) Scalar Quantities – Italics V = 3.5m/s (speed)

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How do we keep track of Vectors? Diagrams – representation of the physical situation Arrows – point in the direction of the vector See page 82

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What is a Resultant? A vector that represents the sum of two or more vectors.

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What are the Properties of Vectors? Vectors can be moved parallel to themselves in a diagram. Vectors can be added in any order To subtract a vector, add its opposite Multiplying or dividing vectors by scalars results in vectors.

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Scalar or Vector Complete Problem One Page 85 of Holt Physics text book Extra Credit: Problem Five Critical Thinking

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How can we determine the resultant magnitude and Direction? Pythagorean Theorem Resultant magnitude

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Tangent Function Tangent Function: tan(θ) = Opposite / Adjacent Inverse Tangent Function: θ = tan -1 Opposite / Adjacent direction

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Sample Problem A An Archaeologist climbs the Great Pyramid in Giza, Egypt. The pyramid’s height is 136m and its width is 230m. What is the magnitude and the direction of the displacement of the archaeologist after she has climbed from the bottom of the pyramid to the top?

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Problem Solving Practice A – Problems 1- 4; page 89 of text

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Enrichment In mathematics, the components of a vector are called projections. The x component is the projection of the vector along the x-axis, and the y component is the projection of the vector along the y-axis.

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Closure What are the two ways to determine magnitude and direction? Which way is simpler?

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Homework Read pages 90 & 91 Complete Problem # 1 on page 92 This information can be found on engrade.com/ due tomorrow at the beginning of class.

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(Mathematical Addition of Vectors)

(Mathematical Addition of Vectors)

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