Transcript Vector addition ppt

Vector Addition
The basics
What is a vector?
• Any value that requires a magnitude and
direction.
• Examples we have already used this year
▫ Velocity
▫ Displacement
▫ Acceleration
• New example
▫ Force: a push or pull on an object
▫ Force unit: Newton (N)
How to show a vector
• Drawn as an arrow
▫ Length of represent the magnitude of the vector.
▫ Arrow points in the correct direction.
• Individual vectors are called COMPONENTS
• The sum of 2 or more vectors is called a
RESULTANT. (A resultant is one vector that
represents all the components combined.)
Representing Direction
• Draw the arrow pointing in the correct direction.
North
West
East
South
•North is up
•South is down
•East is right
•West is left
Vector in One Dimension
So far we have only dealt with vector in the same
plane.
Walk 10m to the right and then 5 m more to the right
10 m + 5 m
=
15 m
When 2 vectors are in the same direction
add the values and keep the same
direction!
Vector in One Dimension
Walk 10m to the right and then 5 m more to the left
10 m
5m
=
5m
When 2 vectors are in opposite directions
subtract the values and keep the direction of
the bigger value.
Between the basic directions
• If your vector is exactly between 2 basics
directions both will be named.
▫ Northeast
N
▫ Southeast
▫ Northwest
▫ Southwest
E
W
S
Direction not exactly between
• Start pointing toward the last written direction.
• Turn the number of degrees given toward the 1st
written direction.
N
For example: 30˚ north of west
• Start west
• and turn 30˚to north
E
W
S
Direction not exactly between
• Start pointing toward the last written direction.
• Turn the number of degrees given toward the 1st
written direction.
N
For example: 55˚ south of east
• Start east
• and turn 55˚to south
E
W
S
Vectors in 2 Dimensions
• Vectors that are in two different directions that
meet at an angle to each other.
• This requires The use of Pythagorean theorem
and trigonometric functions.
+
3m
5m
4m
=
53° N of E
Right Triangles
a2+b2=c2
SOH CAH TOA
Sin A = a/c
Cos A =b/c
Tan A = a/b
Pythagorean Theorem
(3m)2 + (4m)2 =R2
R = 5m
Tan θ= 4m/3m
Tan-1(4/3)
θ=53°N of E