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Vector Mathematics

Why?

- One can add 23 kg and 42 kg and get 65 kg.
- However, one cannot add together 23 m/s south and

42 m/s southeast and get 65 m/s south-southeast. - Vectors addition takes into account adding both

magnitude and direction

Words

- Vector A measured quantity with both magnitude

and direction - Scalar A measured quantity with magnitude only
- Resultant Vector The final vector of a vector

math problem

Vector addition

- Two Ways
- Graphically Draw vectors to scale, Tip to Tail,

and the resultant is the straight line from start

to finish - Mathematically Employ vector math analysis to

solve for the resultant vector

Graphically 1-D

- A 5.0 m east
- B 2.0 m east
- Solve A B

Start

R

R 7.0 m east

Graphically 2-D Right

- A 5.0 m East
- B 5.0 m North
- Solve A B

R

R7.1 m Northeast

Start

But what if

- the vectors are not equal in length initially

and not at right angles. NE would not make

sense. Therefore we need a better coordinate

system!

Compass Coordinate System

N 0º

E 90º

W 270º

S 180º

(No Transcript)

Math (general) Coordinate System

90º

180º

0º

270º

Polar Coordinate System

(No Transcript)

Polar ?? Math

r

y

?

x

(No Transcript)

Lets get back to adding

- Go back to the previous examples and assign

general angle (math) and polar directions then

solve mathematically

Important

- You can add vectors in any order and yield the

same resultant.

Try this one

(No Transcript)

What?!?

- The math you used previously doesnt work (and I

wont let you use the Law of Sines or Cosines) or

does it??? - What we will do is break each vector into

components - The components are the x and y values of the

polar coordinate (go back 6 slides) - Check out the next slide

(No Transcript)

The Table Method

- We will organize these components in a table.
- See the board for this part.

Subtracting Vectors

- Simply add or subtract 180 (keep ? between 0

and 360) to the direction of the vector being

subtracted - You just ADD the OPPOSITE vector (there is no

subtraction in vector math) - Or subtract the proper component in the table

Subtracting Vectors

Relative Velocity

- Read Ch 3
- pp 81 - 94

- HW due on test day
- P 85 1, 5
- P 89 1 4
- P 92 3, 4
- P 94 C 1 - 4

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