1. Vector Addition And Distance vs. Displacement

2. Distance and Displacement In Physics there is a difference between distance and displacement. Distance: The length of the route travelled between two points. Displacement: The shortest path between two points.

3. Distance vs. Displacement Look at the following map:

4. Distance vs. Displacement The Distance is how many km the boat travels to get to the treasure…

5. Distance vs. Displacement The Displacement is how many km it is from the ship to the treasure in a straight line:

6. Distance vs. Displacement Distance is often larger than Displacement. Sometimes they may be equal, though.

7. Distance vs. Displacement Distance > Displacement.

8. Distance vs. Displacement Distance = Displacement

9. Displacement & Vectors Vectors can be connected together to create a “map” similar to the treasure map:

10. Displacement & Vectors Connecting vectors like this is called “Vector Addition”:

11. Displacement & Vectors When vectors are added together the “answer” is the displacement. Adding vectors together can also be called “resolving vectors”

12. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. N Start the first vector from the origin. WE S 3cm

13. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. N Start the second vector from the end of the first WE S 3cm

14. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. N Draw the resultant and calculate the length/angle. WE S 3cm

15. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NThe length can be found using the Pythagorean Theorem: a 2 + b 2 = c 2 WE S 3cm

16. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. N a 2 + b 2 = c 2 (3cm) 2 + (3cm) 2 = c 2 WE S 3cm (b) 3cm (a) c

17. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. N a 2 + b 2 = c 2 (3cm) 2 + (3cm) 2 = c 2 18 cm 2 = c 2 4.24 cm = c WE S 3cm (b) 3cm (a) c

18. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NThe angle can be found using what we know about triangles and trig. WE S 3cm (b) 3cm (a) c = 4.24 cm

19. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NFirst, lets find this angle:. WE S 3cm 4.24 cm

20. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NTo get the angle we use one of the trig identities: sinθ WE S 3cm 4.24 cm θ

21. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. N WE S 3cm 4.24 cm θ

22. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NBut remember, the vector angle is measured from the East-West Axis: WE S 3cm 4.24 cm Θ=45˚

23. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NSince the angle between North and East is 90˚, we can say: 90˚-45˚=45˚ WE S 3cm 4.24 cm Θ=45˚

24. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NNow we have the length and the angle so: Answer: 4.24cm, 45˚NE WE S 3cm 4.24 cm 45˚ Θ=45˚

25. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NReview: If you walked 3 cm N and 3 cm E, what is the distance traveled? Displacement? WE S 3cm (b) 3cm (a) c = 4.24 cm

26. Adding Vectors Resolve the following vectors: 3cm due N and 3cm due East. NReview: If you walked 3 cm N and 3 cm E, what is the distance traveled? 3cm + 3cm = 6 cm Displacement? 4.24 cm WE S 3cm (b) 3cm (a) c = 4.24 cm