1 / 13

Vectors

Vectors. How do vectors combine into a resultant. Vector Diagrams. Vector diagrams are diagrams which depict the direction and relative magnitude of a vector quantity by a vector arrow. Vectors: Motion.

elina
Télécharger la présentation

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. Vectors How do vectors combine into a resultant

  2. Vector Diagrams • Vector diagrams are diagrams which depict the direction and relative magnitude of a vector quantity by a vector arrow

  3. Vectors: Motion • the size of the velocity vector is increasing, so the diagram is depicting a motion with increasing velocity

  4. Scalars and Vectors • Scalars are quantities which are fully described by a magnitude alone. • Vectors are quantities which are fully described by both a magnitude and a direction

  5. Distance and Displacement • Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. • Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position

  6. Graphical (Scale method) and Analytical (Pythagorean) • C 2 = a 2 + b 2 • C 2 = (11 km) 2 + (11 km) 2 • C 2 = 242 km 2 • C = 15.6 km

  7. Example Vector Problem • A motorboat heads due east at 16 m/s across a river that flows due north at 9.0 m/s. • What is the resultant velocity of the boat? • If the river is 136 m wide, how long does it take the motorboat to reach the other side?

  8. Solution : Graphical Method • What is the resultant velocity of the boat?

  9. Solution: Calculation of time • If the river is 136 m wide, how long does it take the motorboat to reach the other side? • V = d/t • 18 m/s = 136 m t • t = 7.56 s

  10. Trigonometric Method • Using the relationship of angles and Trigonometric functions to determine the magnitude of the vectors

  11. Example Problem: Trigonometry • Determine the components of a 20 m displacement 300 northwest. • “a” west component and • “b” north component.

  12. Solution Trigonometry • By choosing the proper component, • a: opposite • b: adjacent • c: resultant • Solve for each component

  13. Summary • Vector addition problems may be solved by 2 methods: • Graphical • Analytical (Pythagorean) • Graphical method depends on a scale and use of angular measurements • Analytical method will use the formulas: • c2 = a2 + b2 • Trigonometry

More Related