So how do we add up a bunch of vectors going all different directions?
(Vector Walk Lab)
Easy: Find the resultant (also known as the displacement):
The shortest distance between two points is just a straight line, and that's your resultant vector (displacement)
This is the same method as adding up the horizontal and vertical components of our vector trip:
Horizontal:
=
Vertical:
=
Place our components tip to tail:
Draw our resulating vector (the Displacement Vector) and we are done!
R
(We could do this with numbers too!)
Draw our resulating vector (the Displacement Vector) and we are done!
25 m
10 m
15 m
R
12 m
8 m
Draw our resulating vector (the Displacement Vector) and we are done!
18 m
25 m
10 m
15 m
R
12 m
8 m
22 m
Draw our resulating vector (the Displacement Vector) and we are done!
18 m
25 m
10 m Pythagorean Thorem:
15 m
(18 m)2 + (22 m)2 = c2
324 m2 + 484 m2 = c2
12 m
808 m2 = c2
8 m
2
√808 m = c
c ≅ 28 m
28 m
22 m
Great Mr. S, but what do we do when they are not right angles? Huh???
a
+
b
I would suggest you take notes like this:
VECTOR ADDITION:
Co
p
y of
d
ia
go
na
l v
ec
to
r
Method 1: Parallelogram method:
Copy of horizontal vector
1) Redraw:
2) Translate:
3) Resolve:
Given:
R
CHECK IT:
Do tips match tips?
Do tails match tails?
(1)
Method 1: Parallelogram method:
Method 1: Parallelogram method:
Tip to tail
Co
py
o
f d
ia
go
na
l v
ec
to
r
Method 1: Parallelogram method:
Copy of horizontal vector
Copy and slide each piece over to make a parallelogram
ec
to
r
Method 1: Parallelogram method:
Co
py
o
f d
ia
go
na
l v
R
Copy of horizontal vector
Draw the resulting vector from the 2 'tails' to the 2 'tips'
ec
to
f d
ia
go
na
l v
R
Co
py
o
Always check to see if vector tips are together and vector tails are together after you draw your resultant!!!
r
Method 1: Parallelogram method:
Copy of horizontal vector
Draw the resulting vector from the 2 'tails' to the 2 'tips'
1) Redraw:
2) Translate:
3) Resolve:
Given:
R
CHECK IT:
Do tips match tips?
Tip­to­Tail:
Do tails match tails?
I would suggest you take notes like this:
VECTOR ADDITION:
Method 2: Component method:
1) Draw perpendicular lines:
2) Use lines and vectors to make boxes:
3) Draw the COMPONENTS of the vectors (x and y that is):
a
by
ay
ax
b
bx
ax, bx = Horizontal Components
ay, by = Vertical Components
4) Add the 'x' and 'y' components:
ay
R
Ry by
bx
ax
(2)
Rx Method 2: Component Method:
a
b
1) Draw perpendicular lines:
a
b
2) Use lines and vectors to make boxes:
a
b
3) Draw the COMPONENTS of the vectors
(x and y that is):
a
ay
ax
ax, bx = Horizontal Components
ay, by = Vertical Components
by
b
bx
4) Add the 'x' and 'y' components:
ay
ax
ax, bx = Horizontal Components
ay, by = Vertical Components
by
bx
So lets do it:
ay
by
bx
ax
So lets do it:
So lets do it:
Ry Rx Components placed tip to tail to find the resultant:
Ry Rx Components placed tip to tail to find the resultant:
R
Rx Ry And we're done!!!
a
+
b
=
R