1. We can break a vector down into 2 vectors. There are many possible ways of doing this for any vector!

5. Resolving Vectors Components of a Vector Any single vector can be split into 2 vectors at right angles to each other. Eg)

6. Resolving Vectors Components of a Vector Any single vector can be split into 2 vectors at right angles to each other. Eg)

7. Resolving Vectors Components of a Vector Any single vector can be split into 2 vectors at right angles to each other. Eg) NOTES p.5

8. Resolving Vectors Components of a Vector Any single vector can be split into 2 vectors at right angles to each other. Eg)

9. vector (x) Horizontal and Vertical Components If these 2 component vectors are in line with the horizontal and vertical planes, we call them “horizontal” and “vertical” components.  H V If we know the size of vector, x, and an angle, , then we can calculate the horizontal & vertical components from soh or cah.

10. vector (x)  H V Here: sin  = opp hyp = V x V = x sin  cos  = adj hyp = H x H = x cos  *In general* adj component = hyp cos  opp component = hyp sin 

11. *In general* adj component = hyp cos  opp component = hyp sin  Examples 50N 60 o 80ms -1 30 o

12. adj component = hyp cos  opp component = hyp sin  Examples 15ms -1 45 o H = opp = 15 sin45 =10.6 m/s V = adj = 15 cos45 =10.6 m/s

13. Problems 14 – 22 (addition of vectors) Problems 23 – 26 (resolving vectors) 14.a) 80km b) 40 km/h c) 20 km, N d) 10 km/h, N 15.a) 70 m b) 50m at 037 0 c) 70 s d) 0.71m/s at 037 0 16.a) 6.8N at 17 0 from 3N (or 13 0 from 4N) b) 11.3N at 45 0 above horizontal (or 45 0 from vertical) c) 6.4N at 39 0 below horizontal (or 51 0 from vertical) 17. 900 km/h, N 18. 26 m/s at 023 0. 19. 804 km/h at 354 0.20. --- (see notes) --- 21.a) 11 km/h b) 5 km/h at 233 0. 22. 4.5 m/s at 063 0 23. 43.3N … reduce the angle! 24. 353.6 N 25. F = 8.66N, a = 43.3 m/s 2 26. Horiz comp. = 5.1m/s, Vert comp = 14.1m/s.

14. Tutorial 1 1.a) 9.9N, 4.95 ms -2 3. a) 4.47ms -1 @ 333 o b) 4ms -1 @ 030 o 4.a) b) 20.5ms -1 @ 73 o from the horizontal Tutorial 2 1a) H – 18.8 ms -1, V – 6.8 ms -1 c) H – 17.7 ms -1, V – 15 ms -1 e) H – 0 ms -1, V – 30 ms -1 2. a) 346N b) 230N c) 11N d) 7.9N e) 3.46N f) 13.8N Problems 14 – 22 (addition of vectors) Problems 23 – 26 (resolving vectors) Tutorial 2 - see HW booklet Q. 1a) c) and e) Q. 2 a) b) c) d) e) f) – see HW booklet Tutorial 1 Q. 1a), 3 and 4 – see HW booklet