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Vectors

Vectors. Ch. 2 Sec 1. Section Objectivies. Distinguish between a scaler and a vector. Add and subtract vectors by using the graphical method. Multiply and Divide vectors by scalers. Scalers and Vectors. A scaler is a quantity that has a magnitude but no direction.

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Vectors

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  1. Vectors Ch. 2 Sec 1

  2. Section Objectivies • Distinguish between a scaler and a vector. • Add and subtract vectors by using the graphical method. • Multiply and Divide vectors by scalers.

  3. Scalers and Vectors • A scaler is a quantity that has a magnitude but no direction. • Ex. Speed, volume, number of pages in a book • A vector is a physical quantity that has both a direction and magnitude. • Ex. Velocity and Acceleration • A resultant vector is the addition of two vectors.

  4. Adding Vectors • Vectors can be added graphically. • A student walks from his house to his friend’s house (a), then from his friend’s house to the school (b). The student’s resultant displacement (c) can be found by using a ruler and a protractor.

  5. Triangle Method • Vectors can be moved parallel to themselves in a diagram. • Thus, you can draw one vector with its tail starting at the tip of the other as long as the size and direction of each vector do not change. • The resultant vector can then be drawn from the tail of the first vector to the tip of the last vector. • Show Clip 580

  6. Properties of Vectors • Vectors can be added in any order. • To subtract a vector add its opposite. • Multiplying or dividing vectors by scalers results in vectors.

  7. Subtraction of Vectors • Show 581

  8. Multiplication of Vectors • Show 582

  9. Homework • P 85 • 1- 5 • P 108 • 1 – 9, 11, 12

  10. Vectors Part II Chapter 3 Section 2

  11. Section Objectives • Identify appropriate coordinate systems for solving problems with vectors • Apply Pythagorean theorem and tangent function to calculate the magnitude and direction of a resultant vector. • Resolve vectors into components using sine and cosine functions • Add vectors that are not perpendicular

  12. Determining resultant Magnitude and Direction • In section one, the magnitude and direction were found graphically. • This is very time consuming and not very accurate. • A simpler method uses Pythagorean theorem and the tangent function.

  13. Use the Pythagorean Theorem to find magnitude of the resultant • If a tourist was climbing a pyramid in egypt. The tourist knows the height and width of the pyramid and would like to know the distance covered in the climb from the bottom to the top. • c = the distance covered • b = The width of the pyramid • a = The height of the pyramid.

  14. Use the tangent Function to find the direction of the resultant • To find the direction remember to take the inverse tangent.

  15. Sample Problem A • An archaeologist climbs the Great Pyramid in Giza, Egypt. The pyramid’s height is 136 m and its width is 2.3 x 102 m. What is the magnitude and direction of the displacement of the aechaeologist after she climbs from the bottom of the pyramid to the top. • First draw a picture. • Given • h = 136 • w = 2.3 x 102 m • Find magnitude and angle

  16. Vector Components • The horizontal and vertical values for a vector are called its components. • x component is parallel to the x-axis • y component is parallel to the y-axis • To find the components use the sine and the cosine. • cos θ = adj/hyp; usually x • sin θ = opp/hyp; usually y

  17. Sample Problem • Find the components of the velocity of a helicopter traveling 95 km/hr at an angle of 35° to the ground. • Given • V = 95 km/h • Θ = 35 ° • Unknown • vx = ? • Vy = ?

  18. Clip 585

  19. Sample problem • A hiker walks 27.0 km from her base camp at 35° south of east. The next day, she walks 41.0 km in a direction 65° north of east and discovers a forest ranger’s tower. Find the magnitude and direction of her resultant displacement

  20. Homework • Page 89 • 1-4 • Page 92 • 1-4 • Page 94 • 1-4 • Section Review 2, 3 • Page 109 • 14,15, 21 - 26

  21. Chapter 3 Section 3.3 Projectile Motion

  22. Section Objectives • Recognize examples of projectile motion. • Describe the path of a projectile as a parabola. • Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion.

  23. Projectiles • Objects that are thrown or launched into the air and are subject to gravity are called projectiles. • Projectile motion is the curved path that an object follows when thrown, launched,or otherwise projected near the surface of Earth. • If air resistance is disregarded, projectiles follow parabolic trajectories.

  24. Projectiles • Projectile motion is free fall with an initial horizontal velocity. • The yellow ball is given an initial horizontal velocity and the red ball is dropped. Both balls fall at the same rate. • In this book, the horizontal velocity of a projectile will be considered constant. • This would not be the case if we accounted for air resistance.

  25. Kinematic Equations for Projectiles • In the vertical direction, the acceleration ay will equal –g (–9.81 m/s2) because the only vertical component of acceleration is free-fall acceleration. • In the horizontal direction, the acceleration is zero, so the velocity is constant.

  26. Classwork • P101 1 S.R. • P 109 27 - 30

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