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We can break a vector down into 2 vectors. There are many possible ways of doing this for any vector!
Resolving Vectors
Components of a Vector
Any single vector can be split into 2 vectors at right angles to each other.
Eg)
Resolving Vectors
Components of a Vector
Any single vector can be split into 2 vectors at right angles to each other.
Eg)
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
Resolving Vectors
Components of a Vector
Any single vector can be split into 2 vectors at right angles to each other.
Eg)
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.
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
*In general*
adj component = hyp cos
opp component = hyp sin
Examples
50N
60o
80ms -130o
adj component = hyp cos
opp component = hyp sin
Examples
15m
s-
145o
H = opp = 15 sin45
=10.6 m/s
V = adj = 15 cos45
=10.6 m/s
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, N15.a) 70 m b) 50m at 0370 c) 70 s d) 0.71m/s at 0370 16.a) 6.8N at 170 from 3N (or 130 from 4N) b) 11.3N at 450 above horizontal (or 450 from vertical) c) 6.4N at 390 below horizontal (or 510 from vertical) 17. 900 km/h, N 18. 26 m/s at 0230.19. 804 km/h at 3540.20. --- (see notes) ---21.a) 11 km/h b) 5 km/h at 2330.22. 4.5 m/s at 0630 23. 43.3N … reduce the angle!24. 353.6 N 25. F = 8.66N, a = 43.3 m/s2
26. Horiz comp. = 5.1m/s, Vert comp = 14.1m/s.
Tutorial 1
1.a) 9.9N, 4.95 ms-2 3. a) 4.47ms-1 @ 333o b) 4ms-1 @ 030o
4.a) b) 20.5ms-1 @ 73o 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
