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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.

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Vectors

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  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

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