Transcript Slide 1

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)
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)
Resolving Vectors
Components of a Vector
Any single vector can be split into 2 vectors at
right angles to each other.
Eg)
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.
q
V
H
If we know the size of vector, x, and an angle, q,
then we can calculate the horizontal & vertical
components from soh or cah.
q
Here:
H
opp
V
sin q = hyp = x
adj
H
cos q = hyp = x
V
V = x sin q
H = x cos q
*In general*
adj component = hyp cos q
opp component = hyp sin q
*In general*
adj component = hyp cos q
opp component = hyp sin q
Examples
60o
30o
adj component = hyp cos q
opp component = hyp sin q
Examples
45o
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, N
15.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.
Problems 14 – 22 (addition of vectors)
Problems 23 – 26 (resolving vectors)
Tutorial 1 Q. 1a), 3 and 4 – see HW booklet
Tutorial 2 - see HW booklet
Q. 1a) c) and e)
Q. 2 a) b) c) d) e) f) – see HW booklet
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
e) H – 0 ms-1, V – 30 ms-1
e) 3.46N
f) 13.8N
c) H – 17.7 ms-1, V – 15 ms-1
2. a) 346N b) 230N c) 11N d) 7.9N