many directions where to go
by ﬂickr user regolare
The Tools of the Trade: Some Trigonometric Equations ...
The Pythagorean Theorem The Sine Law
A c b
c B C
SAS The Cosine Law SSS
Some Useful Properties of Angles ...
When two lines intersect, the angles opposite
each other at the point of intersection are
a° Mnemonic: X
Angles on alternate sides of a transversal are
Angles on coresponding sides of a transversal
ABCD is a parallelogram with AD = DE. Each
segment in the diagram is a vector. Answer the
(a) Name a vector (b) Name a vector that
that is equal to AD is the opposite of AB
(d) Name a vector that is parallel
(c) Name a vector that
to but not equal to EA or EB
is collinear with BA
State the magnitude and direction of each vector.
State the magnitude and direction of each
vector. (You can determine the answer using ruler and protractor.)
Draw scale diagrams of the following vectors using pencil,
ruler, protractor, and paper. Label the diagram. Be sure to
indicate the scale you used.
(a) Tiffany walks 13 blocks in a direction E15°S.
(b) A boat is headed 300° at 45 km/h.
Adding Vectors Using Scale Diagrams ...
A vector is represented by an arrow. It's LENGTH determines it
MAGNITUDE and the TIP determines its DIRECTION.
When a vector is moved around in a
plane it is considered to be the same
vector. These two vectors are TAIL
considered to be identical:
Vectors can be added an any order.
When two vectors are added a new vector is made. It is
called the RESULTANT vector.
a means quot;vector aquot;
a means quot;magnitude of vector aquot;
There are two techniques that we use to add vectors using a
scale diagram ...
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.
Visualizing the Process ...
Sketch two vectors to represent the two velocities.
The Triangle Method
Resultant of Forces
(Addition of Vectors)
The Triangle Method ...
We use the triangle method when the vectors are arranged tip-to-tail.
Scale: 1 cm = 2 km
23.4 km 59° S of E
11.7 cm 59° S of E
Remember, we use measurements with a ruler and protractor to ﬁnd
You try ...
Add each pair of vectors using the triangle method.
is 3 meters east
is 3 meters southwest
is 4 meters north
is 4 meters west