subtracting vectors a – b = ?. example problem what is 30 m/s north minus 15 m/s east?
TRANSCRIPT
![Page 1: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/1.jpg)
Subtracting Vectors
A – B = ?
![Page 2: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/2.jpg)
Example Problem
What is 30 m/s north minus 15 m/s east?
![Page 3: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/3.jpg)
Example Problem
What is 30 m/s north minus 15 m/s east?
Question:
How many vectors are there in this problem?
![Page 4: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/4.jpg)
Example Problem
What is 30 m/s north minus 15 m/s east?
Question:
How many vectors are there in this problem?
![Page 5: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/5.jpg)
Words Math
What is 30 m/s north minus 15 m/s east?
north30A sm
east15B s
m
![Page 6: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/6.jpg)
What is 30 m/s north minus 15 m/s east?
north30A sm
Mathematically
east15B sm
A – B = ?
Words Math
![Page 7: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/7.jpg)
What is 30 m/s north minus 15 m/s east?
north30A sm
Mathematically
east15B sm
A – B = ?
Words Math
The Problem: We only know how to add vectors.
![Page 8: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/8.jpg)
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
![Page 9: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/9.jpg)
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
Guess: what is – B?
![Page 10: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/10.jpg)
Time Out!
C
This is C
![Page 11: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/11.jpg)
Time Out!
C
Point in the direction of – C!
![Page 12: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/12.jpg)
Time Out!
C
Point in the direction of – C!
![Page 13: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/13.jpg)
Time Out!
C
Point in the direction of – C!
- C
![Page 14: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/14.jpg)
Continue
![Page 15: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/15.jpg)
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
- B is B in the opposite direction
![Page 16: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/16.jpg)
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
A – B = A + (– B)
- B is B in the opposite direction
![Page 17: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/17.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1 cm = 5 m/s
![Page 18: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/18.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Which are tip-to-tail?
3)
2)
4)
![Page 19: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/19.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Which are tip-to-tail?
3)
2)
4)
![Page 20: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/20.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Draw the resultant for 1):
from point ___ to point ___?
2)
• c
• ba •
![Page 21: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/21.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Draw the resultant for 1):
from point ___ to point ___?
2)
• c
• ba •
ac
![Page 22: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/22.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Draw the resultant for 2):
from point ___ to point ___?
2)
• f
d •
e •
![Page 23: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/23.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Draw the resultant for 2):
from point ___ to point ___?
2)
• f
d •
e •
f d
![Page 24: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/24.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1)
Notice: the resultant is the same for option 1) and option 2).
2)
![Page 25: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/25.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
1 cm = 5 m/s
(6.70)(5) m/s = 33.5 m/s
6.70 cm
![Page 26: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/26.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
63˚
![Page 27: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/27.jpg)
Graphical Addition of Vectors
1. Make a scale drawing.2. Move the vectors tip-
to-tail.3. Draw the resultant
vector (free tail to free tip).
4. Measure the length of the resultant with a ruler.
5. Measure the direction of the resultant with a protractor.
A + (– B)
33.5 m/s @ 63˚ north of west
1 cm = 5 m/s
63˚
Your final answer!
![Page 28: Subtracting Vectors A – B = ?. Example Problem What is 30 m/s north minus 15 m/s east?](https://reader036.vdocuments.site/reader036/viewer/2022062515/56649cae5503460f9497225f/html5/thumbnails/28.jpg)
Motion Notes (Continued):
10. Subtracting Vectors a. The negative sign makes one vector point in
the opposite direction.
i. Ex: BA
B
has the same magnitude as B
and the opposite direction
b. Deal with the directions, then add the vectors.
i. )B(ABA