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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. Let’s say you draw an arrow. How long is it?. 60 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. Let’s say you draw an arrow. How long is it? 60 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. Recall: Magnitude without direction is called a scalar.

  6. ScalarVector Distance Displacement Speed Velocity Time Acceleration

  7. 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?

  8. Add vectors head to tail. The arrow is the head, the other end is the tail. 2 m east + 3 m east Resultant 5 m east

  9. Head to Tail Vector Addition

  10. 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

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

  12. Use the Pythagorean Theorem to find the magnitude of the resultant.

  13. What is the resultant magnitude of 3 m east + 4 m north? The magnitude = 5 m 4 m 3 m

  14. To find direction: Find the angle of the resultant and name the direction. Find the angle closest to the starting point (where 2 tails meet). Use inverse tangent θ = tan-1 (4/3) = 53.1° 4 m θ 3 m

  15. For direction, it’s always the 2nd direction ‘of’ the 1stdirection. In this case, the 1st direction traveled is East, the 2nd direction is North. Therefore the direction is N of E. The resultant is: 5m @ 53.1° N of E 4 m θ 3 m

  16. Example for adding more than 2 vectors together: http://www.physicsclassroom.com/class/vectors/U3l1eb.cfm

  17. A boat heads west across a 300 m wide 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 @ 26.6° S of W How long does it take to cross the river? 30s How far downstream does the boat travel? 150 m

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