Vectors!!!

Magnitude

Unit

Direction

Magnitude

Unit

Point to remember.

the magnitude of a vector is ALWAYS positive

the direction can be negative however.

Vectors graphically

A vector is a magnitude and direction

Are these two vectors

the same?

How about these two?

Adding Vectors graphically

A

B

Tail-to-tip method

A

B

A

B

C

C = A + B

A bit to note:

When is this true

Another special case

A

B

C

Pythagorean theorem

**THIS IS KEY**

This is big, the next ~7 chapters use this

We will introduce it today, and work on it

with application on Wednesday too.

Y

X

V

V

V

y

x

The idea is that every vector has

components (parts) that are in the

direction of the x and y axis.

O

Now for a bit of Trig review

O

Hypotenuse

Opposite side

Adjacent side

O

5

4

3

A. 3/4 B. 3/5 C. 4/5 D. 4/3 E.5/4

What is the cosine of theta?

What is the tangent of theta?

V

y

V

y

V

x

V

x

V

V

V

V

Sin =

Tan =

= Sin

= Cos

O

O

O

O

V

x

V

Cos =

O

y

A

B

B

A

x

x

Y

Y

B

A

x

x

A

Y

C

x

C

Y

C

B

Y

**How many of these quantities do you need to define a vector?**

A. 1 B. 2. C. 3 D. 4 E. depends

A. 1 B. 2. C. 3 D. 4 E. depends

Vectors have:

Scalars have:

Review: Vectors and Scalars

What is this equation saying?

Another special case

A

B

C

Pythagorean theorem

Vectors: By components

Main Ideas

Vector vs. Scalar

Adding vectors as pictures, graphically, as arrows.

Math with Vectors

Adding vectors by components

Trigonometry

Projectile motion

Relative Velocity

Scalars multiply vectors

A

2A

.5A

-2A

Two big assumptions:

Ax = 0

Ay = -g = -9.8 m/s^2

Projectile motion

To describe fully this motion

they will give two terms

Launch angle

Launch speed

**Relative motion**

key points

Observers

measure things

can move

Constant velocity

a=0

Directions

x and y separate

Relativity is all about your point of view,

better it is about your measurement compared to someone else.

The person on the ground sees a train going 9 m/s east.

A passenger on the train is walking at 2 m/s east.

How fast does the person on the ground view the passenger?

**Note the subscripts:**

first letter=object

second letter = reference frame

let them form own relationship

BG ~ BT+TG ~ PG

if center two equal cut them out, and splice

first letter=object

second letter = reference frame

let them form own relationship

BG ~ BT+TG ~ PG

if center two equal cut them out, and splice

**The final point of relative motion is**

Vab = - Vba

The magnitudes the same, direction opposite.

Vab = - Vba

The magnitudes the same, direction opposite.

These two sets say the same thing.

The magnitude of a competent of a vector must be:

a) less than or equal to the magnitude of the vector

b)equal to the magnitude of the vector.

c)greater than or equal to the magnitude of the vector

d)less than, equal to, or greater than the magnitude of the vector

"I .. am,.. so lost with the adding and multiplying vectors. "

" I would like to go over resolving components of vectors a little more. "

"what is the easiest way to distinguish between scalars and vectors and know which one we are using or talking about in a problem?"

"Can you further explain relative velocity?"

"How do you find the components of a vector?"

If my velocity vector has a magnitude of 3.0 m/s

and it is at an angle of 30 degrees north of east

how much of the vector is in the 'y' direction?

a) 3.0 m/s

b) 2.6 m/s

c) 1.5 m/s

d) 0.0 m/s

e) no idea, please do this and quiz me again.

If my acceleration vector has a magnitude of 4.0 m/s^2

and it is at an angle of 30 degrees west of North

how much of the vector is in the 'x' direction?

a) 3.5 m/s^2

b) 2.0 m/s^2

c) -2.0 m/s^2

d) -3.5 m/s^2

e) 4.0 m/s^2

f)-4.0 m/s^2

"The book's definition of magnitude is a little hazy. How do you define it?"

Walk north 20 m, then walk east 10 m. Where are you?

time at 5 s, then 10 s. later, when is it?