applied 40s april 29, 2009
DESCRIPTION
Introduction to vector addition.TRANSCRIPT
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Vector Addition
many directions where to go by flickr user regolare
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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
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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
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TRANSVERSALTRANSVERSAL
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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
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State the magnitude and direction of each vector.
HOMEWORK
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State the magnitude and direction of each vector. (You can determine the answer using ruler and protractor.)
HOMEWORK
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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
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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"→
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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
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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
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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