1 / 31

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

zenia-chaney
Download Presentation

3.1 Introduction to Vectors

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related