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Vector Basics

Vector Basics. OBJECTIVES. CONTENT OBJECTIVE: TSWBAT read and discuss in groups the meanings and differences between Vectors and Scalars LANGUAGE OBJECTIVE: TSW read and discuss the key vocabulary words Vectors and Scalars and Resultants. Scalar.

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Vector Basics

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  1. Vector Basics

  2. OBJECTIVES • CONTENT OBJECTIVE: TSWBAT read and discuss in groups the meanings and differences between Vectors and Scalars • LANGUAGE OBJECTIVE: TSW read and discuss the key vocabulary words Vectors and Scalars and Resultants.

  3. Scalar • Scalar quantities only have magnitude (size represented by a number & unit) ex. Include mass, volume, time, speed, distance

  4. Vectors • Vector quantities have magnitude and direction. Ex. Include force, velocity, acceleration, displacement

  5. Vector Representation • Vectors are represented as arrows • The length of the vector represents the magnitude start end head or tip tail

  6. Ex. 1.0 cm = 1.0 m/s Draw a 3.0 m/s East vector Vector will be 3.0 cm long Ex. 1.0 cm = 1.5 m/s Draw a 3.0 m/s East vector Vector will be 2.0 cm long Vectors are always drawn to a scale comparing the magnitude of your vector to the metric scale

  7. Direction of Vectors • Direction of vectors is represented by the way the arrow is pointed • Vector components are based on coordinate plane so vectors can point in negative or positive directions N Negative X, Positive Y Positive X, Positive Y W E Negative X, Negative Y Positive X, Negative Y S

  8. Resultant Vectors • A resultant vector is produced when two or more vectors combine • If vectors are at an angle, vectors are always drawn tip to tail

  9. 3 m east 14 m east 11 m east Adding and subtracting vectors – Same Direction • If the vectors are equal in direction, add the quantities to each other. • Example: the resulting vector is

  10. 3 m west 8 m east 11 m east Adding and subtracting vectors – Opposite Directions • If the vectors are exactly opposite in direction, subtract the quantities from each other. • Example: the resulting vector is

  11. Vectors at Right Angles to each other • If vectors act at right angles to each other, the resultant vector will be the hypotenuse of a right triangle. • Use Pythagorean theorem to find the resultant

  12. Pythagorean Theorema2 + b2 = c2 where c is the resultant Hypotenuse = resultant vector c a b

  13. Example: • A hiker leaves camp and hikes 11 km, north and then hikes 11 km east. Determine the resulting displacement of the hiker.

  14. 11 km east 11 km north R 112 + 112 = R2 121 + 121 = R2 242 = R2 R = 15.56 km, northeast

  15. Calculating a resultant vector • If two vectors have known magnitudes and you also know the measurement of the angle (θ) between them, we use the following equation to find the resultant vector. • R2 = A2 + B2 – 2ABcosθ Use this for angles other than 90º Make sure your calculator is set to DEGREES! (go to MODE)

  16. Example 1: R 4.0 N, SW • θ = 110° • R2 = 5.02 + 4.02 – 2(5.0)(4.0)(cos 110) • R2 = 54.68 • R = 7.39 N, Southwest 5.0 N, W θ

  17. R 4.3 m θ 5.1 m Example 2: θ = 35º • R2 = 4.32 + 5.12 – (2)(4.3)(5.1)(cos 35) • R2 = 8.57 • R = 2.93 m, northwest

  18. Vector Equations • Pythagorean Theorema2 + b2 = c2 where c is the resultant • Law of Cosines R2 = A2 + B2 – 2ABcosθ

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