subtracting vectors a – b = ?. example problem what is 30 m/s north minus 15 m/s east?
TRANSCRIPT
Subtracting Vectors
A – B = ?
Example Problem
What is 30 m/s north minus 15 m/s east?
Example Problem
What is 30 m/s north minus 15 m/s east?
Question:
How many vectors are there in this problem?
Example Problem
What is 30 m/s north minus 15 m/s east?
Question:
How many vectors are there in this problem?
Words Math
What is 30 m/s north minus 15 m/s east?
north30A sm
east15B s
m
What is 30 m/s north minus 15 m/s east?
north30A sm
Mathematically
east15B sm
A – B = ?
Words Math
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.
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
Guess: what is – B?
Time Out!
C
This is C
Time Out!
C
Point in the direction of – C!
Time Out!
C
Point in the direction of – C!
Time Out!
C
Point in the direction of – C!
- C
Continue
north30A sm
east15B s
m
The Trick: Make it Addition
A – B = A + (– B)
- B is B in the opposite direction
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
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
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)
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)
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 •
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
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 •
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
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)
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
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˚
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!
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