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3.1 Introduction to Vectors

3.1 Introduction to Vectors. Page 82. Section Objectives. Distinguish between a vector and a scalar. Add and subtract vectors by using the graphical method. Scalar Quantities. Scalars can be completely described by magnitude (size) Scalars can be added algebraically

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3.1 Introduction to Vectors

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  1. 3.1 Introduction to Vectors Page 82

  2. Section Objectives • Distinguish between a vector and a scalar. • Add and subtract vectors by using the graphical method.

  3. Scalar Quantities • Scalars can be completely described by magnitude (size) • Scalars can be added algebraically • They are expressed as positive or negative numbers and a unit • examples include: mass, electric charge, distance, speed, energy

  4. Vector Quantities • Vectors need both a magnitude and a direction to describe them (also a point of application) • They need to be added, subtracted and multiplied in a special way • Examples :- velocity, weight, acceleration, displacement, momentum, force

  5. Distinguish between a scalar and a vector. • The acceleration of a plane as it takes off. • The duration of a flight. • The displacement of the flight • The amount of fuel required for the flight. • The force acting on the plane in the form of air resistance.

  6. 3.2 Vector Operations Page 86

  7. Section Objectives • Calculate the magnitude and direction of a resultant vector. • Resolve vectors into components. • Add vectors that are not perpendicular.

  8. Terminology • Two or more vectors can be combined together to form a resultant • A vector that does not lie along the x or y-axis may be resolved into its components

  9. Calculate the magnitude and direction of a resultant vector. • Draw 20 south of west. • Draw 20 west of south.

  10. Calculate the magnitude and direction of a resultant vector. • Use the Pythagorean Theorem to find the magnitude of the resultant.

  11. Calculate the magnitude and direction of a resultant vector. • Use SOHCAHTOA to find the direction of the resultant.

  12. Resolve vectors into components. • Every vector can be resolved into its x and y components using trigonometry. • If a vector is located on the x or y axis, then the other component of that vector is zero.

  13. Resolve vectors into components.

  14. Add vectors that are NOT perpendicular • If the original displacement vectors do not form a right triangle • 1. Resolve each vector into its x- and y-components • 2. Find the sum of the x- and y-components • 3. Use the Pythagorean Theorem to find the magnitude of the resultant • 4. Use the tangent function to find the direction of the resultant

  15. Adding non-perpendicular vectors

  16. Adding non-perpendicular vectors

  17. Practice #1 • 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 between the base camp and the tower.

  18. Check you work! • Page 89 1. a) 23 km b) 17 to the east 2. 45.6 m at 9.5° east of north 3. 15.7 m at 22° to the side of downfield 4. 1.8 m at 49° below the horizontal

  19. Check your work! • Page 92 1. 95 km/h 2. 44 km/h 3. x=21 m/s, y=5.7 m/s 4. x=0 m , y=5m

  20. Practice #1 • A bullet travels 85 m before it glances off a rock. It ricochets off the rock and travels for an additional 64 m at an angle of 36 degrees to the right of its previous forward motion. What is the displacement of the bullet during this path.

  21. Make physics YOUR business. Try problems 1-4 on pages 94.

  22. Dr. Miller says: Time for some practice! Try pages 89 & 92.

  23. Check your work! • Page 94 1. 49 m at 7.3° to the right of downfield 2. 7.5 km at 26° above the horizontal 3. 13.0 m at 57° north of east 4. 171 km at 34° east of north

  24. Problem 3C 1. 216.5 m at 30.0 north of east 2. 2.89 Χ 104 m at 21.7 above the horizontal 4. 1320 km at 3.5 east of north 5. 221 km at 11.2 north of east

  25. Add and subtract vectors by using the graphical method.

  26. Multiply and divide vectors by scalars. • Multiplying or dividing vectors by scalars results in _________________. • You are in a cab traveling 25 mph east. You tell the cab driver to drive twice as fast. Your new velocity is ____________________. • You are in a cab traveling 25 mph east. You tell the cab driver to drive twice as fast in the opposite direction. Your new velocity is ________________.

  27. Add and subtract vectors by using the graphical method.

  28. Add and subtract vectors by using the graphical method. • T / F Vectors can be added in any order. • T / F Vectors can be moved parallel to themselves in diagrams. • Let’s see: http://www.physicsclassroom.com/mmedia/vectors/ao.cfm

  29. Calculate the magnitude and direction of a resultant vector. • http://www.physicsclassroom.com/Class/vectors/u3l1b.cfm

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