1. Please get a calculator today. 
T4.1b Vectors: I) Find the Horizontal & Vertical Components; II) Find the Resultant of Two Forces Acting on a Point
Please get a calculator today. 

3. OPENER: Given the following vectors, find: (use the Parallelogram Rule on # 3 & #4)b a a
1) -a
2) - b -a 2b a’ b’
4) a – b b b
3) a + b a
–b’
a + (– b) b
a + b –b a
a – b a’

4. Active Learning Assignment?

5. #1 #2 #3 LESSON: I) Find the Horizontal & Vertical Components
We know how to get the resultant from two components, but, how do we get the components from a resultant? (Poor orphaned resultant) “It takes a village to raise a child…”
Which would make the best parents and why? #1 #2 #3
“Because they were right for each other”
-Michael French, Class of 2012

6. The horizontal is 8.6 units and the vertical is 12.3 units.
Ex: Given α = 55° (the direction) and |v| = 15 (the magnitude), find the magnitude of the horizontal and vertical components. ( 1 dec. pl.) y x 15 55 ?
hyp.
opp. (y) ?
adj. (x)
The horizontal is 8.6 units and the vertical is 12.3 units. * * *
Formulas?
*Can say “x value” or “y value” instead

7. The horizontal is 45.8 units and the vertical is 41.8 units.
Try: Given α = 137°40´ and |v| = 62, find the magnitude of the horizontal and vertical components. ( 1 dec. pl.) y 62
Remember to put cos(137°40’) in the calculator as cos( /60)
| y |
137°40´ x
| x |
The horizontal is 45.8 units and the vertical is 41.8 units.

8. * The resultant force is 24.4 newtons. This is Olivia Newton John.
II) Find the Resultant of Two Forces Acting on a Point
Ex: Two forces of 15 newtons and 22 newtons act on a point and the angle between them is 100° . Find the magnitude of the resultant force. ( 1 dec. pl.)
What other pieces of information can we find?
Two things: the resultant does NOT cut the angle in half, and it does not create a right triangle!!!
15 n
22 n
180° – 100° = 80° WHY?
15 n
22 n
100°
80° ?
We can now use the Law of Cosines, SAS. *
The resultant force is 24.4 newtons.
This is Olivia Newton John.

9. The resultant is 50.3 newtons.
Try: Two forces of 25 newtons and 31 newtons act on a point and the angle between them is 52° 40´. Find the magnitude of the resultant force. ( 1 dec. pl.)
Remember to subtract 52°40’ from 180°, use °60’
– 52°40’
25 n
31 n
25 n
31 n
52° 40´.
127° 20´.
The resultant is 50.3 newtons.

10. Active Learning Assignment: Vector I Handout 30-46 evens
Answers are in horizontal (x), then vertical (y). Write answers
47, , lbs.
51, , 6642
, N
39.8, lbs.