applied 40s april 29, 2009

Vector Addition

many directions where to go by flickr user regolare

The Tools of the Trade: Some Trigonometric Equations ...

The Pythagorean Theorem

A

B C

bc

a

The Sine LawA

B C

bc

a

The Cosine LawA

B C

bc

a

SSSSAS

Some Useful Properties of Angles ...

Opposite Angles

a°a° b°b°

When two lines intersect, the angles opposite each other at the point of intersection are congruent.

Mnemonic: X

Alternate Angles

a°

a°b°

b°

Angles on alternate sides of a transversal are congruent.

Mnemonic: Z

Corresponding Angles

a°

a°b°

b°

Angles on coresponding sides of a transversal are congruent.

Mnemonic: F

TRANSVERSALTRANSVERSAL

ABCD is a parallelogram with AD = DE. Each segment in the diagram is a vector. Answer the following questions.

(d) Name a vector that is parallel to but not equal to EA or EB

(c) Name a vector that is collinear with BA

(b) Name a vector that is the opposite of AB

(a) Name a vector that is equal to AD

HOMEWORK

State the magnitude and direction of each vector.

HOMEWORK

State the magnitude and direction of each vector. (You can determine the answer using ruler and protractor.)

HOMEWORK

Draw scale diagrams of the following vectors using pencil, ruler, protractor, and paper. Label the diagram. Be sure to indicate the scale you used.

(b) A boat is headed 300° at 45 km/h.

(a) Tiffany walks 13 blocks in a direction E15°S.HOMEWORK

Adding Vectors Using Scale Diagrams ...

When two vectors are added a new vector is made. It is called the RESULTANT vector.

Vectors can be added an any order.

When a vector is moved around in a plane it is considered to be the same vector. These two vectors are considered to be identical:

A vector is represented by an arrow. It's LENGTH determines it MAGNITUDE and the TIP determines its DIRECTION.

There are two techniques that we use to add vectors using a scale diagram ...

TIP

TAIL

a means "magnitude of vector a"a means "vector a"→

A ball is thrown horizontally against a wall with a velocity of 10 m/s. It rebounds with a velocity that has a magnitude of 75% of the initial velocity. Sketch two vectors to represent the two velocities.Visualizing the Process ...

Resultant of Forces(Addition of Vectors)http://www.walter-fendt.de/ph14e/resultant.htm

The Triangle Method

>

>tip

-to-ta

il

The Triangle Method ...

We use the triangle method when the vectors are arranged tip-to-tail.

Scale: 1 cm = 2 km

Remember, we use measurements with a ruler and protractor to find the "answers."

6cm

10cm

RESULTANTRESULTANT

11.7 cm 59° S of E

23.4 km 59° S of E

HOMEWORK

You try ...

Add each pair of vectors using the triangle method.

is 3 meters eastis 4 meters north is 3 meters southwest

is 4 meters west

Find Find

HOMEWORK