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Vectors

Enduring Understanding: Modeling is widely used to represent physical and kinematic information. Essential Question: What are the practical applications of modeling physical and kinematic information?. Vectors. Draw an arrow. How long is it?. ? cm. 1 cm = 20 miles.

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Vectors

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  1. Enduring Understanding: Modeling is widely used to represent physical and kinematic information. Essential Question: What are the practical applications of modeling physical and kinematic information?

  2. Vectors

  3. Draw an arrow. How long is it? ? cm

  4. 1 cm = 20 miles Now, the original arrow represents something else. How might this be useful?

  5. Vectors are scale model arrow representations. Vectors have magnitude (size) and direction. Magnitude without direction is called a scalar. Give examples of direction.

  6. Direction We will also continue to use (+) and (-) to indicate direction.

  7. ScalarVector Distance Displacement Ex. 25 Miles Ex. 25 Miles South Speed Velocity Give an example of a speed and a velocity. Mass Weight Time Force

  8. Vector Addition The resultant is one vector that represents the addition of two or more vectors. What is the resultant displacement if you add 2 m east to 3 m east?

  9. 2 m east + 3 m east Resultant 5 m east

  10. Head to Tail Vector Addition

  11. Activity – Add the Vectors • On paper: draw diagrams for the addition of the following vectors: • A. 2 m east • B. 4 m north • C. 5 m west • Add the vectors 3 different ways using a scale of 1cm = 1m: • ABC, BAC, CBA • Do you think it matters what order you add the vectors together?

  12. Draw a head to tail vector diagram showing the addition of 10 m north + 5 m south. What is the resultant displacement? 5 m south 10 m north Resultant: 5 m north

  13. What is the resultant of 3 m east + 4 m north? 4 m 3 m

  14. Pythagorean Theorem

  15. What is the resultant magnitude of 3 m east + 4 m north? The magnitude = 5 m How about the direction? We would have to use trigonometry for this but we can give an approximate direction of northeast (NE).

  16. Draw a to scale head to tail diagram representing this problem. What are some real world applications of vector addition?

  17. A boat heads west across a river at 10 m/s. The current pushes the boat south at 5 m/s. What is the resultant speed of the boat? 11.2 m/s How far does the boat travel in 30 s? 336 m

  18. A 40 N force acts to the east as a 60 N force acts to the south. What is the magnitude of the resultant force? 72 N

  19. Vector Representation of Projectile Motion

  20. A vector has magnitude and direction. For each ball, draw vectors to represent the horizontal component of the velocity.

  21. For each ball, draw vectors to represent the vertical component of the velocity.

  22. Try it for this one.

  23. Try it for the one on the left.

  24. Even More Vector Practice • 1) A person walks 5 m to the south. They stop for a rest. They then travel 20 m farther to the south. What was their resultant displacement? 25 m south

  25. 2) Galileo is riding a bicycle and is pedaling at 8 m/s to the west. A 2 m/s wind is pushing to the east. What is the resultant velocity of Galileo and his bicycle? 6 m/s west

  26. 3) A hiker travels 300 m west, stops, checks a map and then travels 700 m north. How far is the hiker from their starting point? 762 m

  27. 4) A boater drives a motorboat out in the bay. The boat has a speed 40 m/s directed west but a current pushes it south at 10 m/s. What is the resultant speed of the boat? 41.2 m/s

  28. 5) How long will it take the boat to travel a distance of 2500 m? 60.7 s

  29. 6) A person walks 40 m east, 20 m south, 10 m west and 40 m north. How far are they from their starting point? 36 m

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