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Vector Addition

Vector Addition. Chapter 4. Objectives Quiz 3. Determine graphically the sum of two or more vectors Solve problems of relative velocity Establish a coordinate system in problems involving vector quantities Use the process of resolution of vectors to find the components of vectors.

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Vector Addition

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  1. Vector Addition Chapter 4

  2. Objectives Quiz 3 • Determine graphically the sum of two or more vectors • Solve problems of relative velocity • Establish a coordinate system in problems involving vector quantities • Use the process of resolution of vectors to find the components of vectors

  3. Objectives Quiz 3 • Determine algebraically the sum of two or more vectors by adding the components of the vectors

  4. Graphical Vector Addition • Done by placing vector lines end to end (in appropriate direction)

  5. Graphical Vector Addition • ------------------ + ------ = ---------- • --- + --- = -------- • ------------------------------------ +  = -------------------------------- What could each of these represent?

  6. Relative Velocity • Using vector addition to arrive at actual speed • How fast compared to what? • A plane can fly at 300 mph with no wind relative to the ground. What is the planes relative velocity when • Has a tail wind of 30 mph? • Has a head wind of 50 mph?

  7. Relative Velocity • A boy can swim at 3.5 m/s in calm water. The boy goes swimming in a river with a current of 1.5 m/s. • If the boy swims upstream, how fast does he move relative to shore? • How fast is the boy moving relative to the water? • Same 2 questions, but downstream

  8. Draw a model • A certain fish can swim 4.6 m/s relative to water that isn’t moving. If there is a current moving at a speed of 1.3 m/s relative to the river bank, how long will it take the fish to swim 200m upstream?

  9. Vectors Addition Algebraically

  10. SOHCAHTOA • Sin Angle = Opposite over Hypotenuse • Cosine Angle = Adjacent over Hypotenuse • Tangent Angle = Opposite over Adjacent • SOHCAHTOA gives us ratios of sides

  11. In this class • We will describe everything in 2 dimensions, North South (Up Down) and East West (Right Left) • Later on if you enjoy physics you can do 3-d models

  12. Describing Angles • 30 degrees N of E or 60 degrees E of N (for left)

  13. Describing Angles • Determine which direction you are closest too (NSEW). This will be your 2nd direction stated • X degrees direction of direction • Determine which direction you are moving away from the line • If North/South, then East/West off of line • X Degrees direction of direction

  14. Describing Angles • Determine how many degrees off the line by using some algebra • X degrees direction of direction

  15. Vector Resolution • A man travels 9 miles north and then travels 12 miles east. • Describe the man’s movement using X degrees direction of direction

  16. Vector Resolution • A bird travels 8 miles south and then travels 6 miles east. • Describe the bird’s movement using X degrees of direction of direction

  17. Magnitude of displacement • Displacement away from origin • Pythagorean (or sohcahtoa) • A2 + B2 = C2 • Add to our description of movement • Blank units at X degrees direction of direction

  18. Vector Resolution • A bird travels 26 miles at 30 degrees E of North. • How many miles North did the bird travel? • How many miles East did the bird travel?

  19. Vector Resolution • A car travels 80 miles at 20 degrees S of E • How many miles South did the car travel? • How many miles East did the car travel?

  20. Combining Vectors • 10 miles North + 10 miles East = Not 20 miles • 10 miles North + 10 miles North = 20 miles North • Combine like terms on following or cancel as needed (North cancels South, East cancels West)

  21. Vector Resolution • A man travels 5 miles north, then travels 4 miles east, then 6 miles west. • Describe the man’s movement using Blank miles X degrees direction of direction

  22. Vector Resolution • A bird travels 7 miles South, then travels 2 miles East, and then 4 miles North • Describe the bird’s movement using Blank miles X degrees direction of direction

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