Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

F13 PH 121 3.3-3.4

No description
by

Richard Datwyler

on 3 May 2018

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of F13 PH 121 3.3-3.4


Vectors!!!
Adding Vectors graphically
A
B
Tail-to-tip method
A
B
A
B
C
C = A + B
Vectors: By components

This is big, the next ~7 chapters use this
We will introduce it today, finishing the chapter
and then jump into application of them on
Wednesday.
This will free Friday for an activity, it would be good to bring your computers on Friday.
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.
Vectors each have a magnitude and a
direction.
Knowing these two thing define a vector.

But there is another way to define a vector
If we know its vector components it is also
defined.
O
Now for a bit of Trig review
That's nice how do I use it?

What do I NEED to make
use of it?
Two things.
Right triangle
Angle
O
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
Unit vector
These are as they are defined
Vectors of length one, unity.

They depend on the coordinate system,
and are very useful for the transformation
between coordinate systems as well as
analysis of questions.
Standard notation for these are:

in the x direction
in the y direction
in the z direction
X
Y
Z
With these unit vectors we can define our
vectors and component vectors as:
Let vectors
A = (3.0 m, 20 degrees south of east),
B = (2.0 m, north)
C = (5.0 m , 70 degrees south of west)
Write A,B,C in component form, and find D=A+B+C.

3.9 m 73 degrees south of east
Let
find the magnitudes and directions of:
E and F
E + F
-E - 2F

3.6, 56.3 degrees north of east
2.8, 45 degrees south of east
4.1, 14 degrees north of east
6.1, 9.5 degrees north of west
Which of these two are easier? Why.

As we do problems in the future, we will
use these two ideas heavily

Practice, Practice Practice

3. 10,11,12,13,14,15,16,21,23,29

Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction.

Write F in component form
Draw all three
What are the magnitude and direction of F?

23 For the three vectors shown:
What is vector B, in components form and magnitude and direction?

C 2
4 A
B
"Could you go over the types of coordinate systems; polar and Cartesian?"
"Can we go over the components of the vectors just a little bit?" "Can you please explain the difference between components and component vectors?"
"why does it say that the resultant vector is the sum of the x and y component vectors when we actually need to use the Pythagorean theorem to find the resultant vector?"
"Are vector components and a vector's magnitude and direction the same thing? Can there be a circumstance where a vector would be decomposed into more than 2 composite vectors?"
"Will you explain a little more on how to use the coordinate systems?"
Full transcript