Thursday
Unit 3: Two dimensional
motion.
Introduction to vectors
Where we’ve been
 We
have studied motion going
horizontally and vertically.
 We have been able to describe an
objects motion using graphs, diagrams,
words, and numbers.
 Let’s review…
Important terms
Displacement
•
Distance is its magnitude
•
Has direction
 Velocity
• Speed is its magnitude
• Has direction

Vector Example
An Airplane flies east at a velocity of 120
km/h. There is a 30 km/h tailwind. What is the
total velocity of the plane?
How would you approach this
problem?
A boy walks 9.0 km north and then 6.5 km
east?
Where we’re going…2D
Motion
Use vectors to describe motion of an object
that is traveling in both the x and y direction.
 Vector components


Two or more vectors acting on the same
point.
Resultant

One vector having the same effect as the
combined components.
Visual of new terms
Y Component
Resultant
X Component
Apples and Oranges
• When adding vectors they
must represent the same
motion
• velocity + velocity
acceleration + acceleration OK
displacement +
displacement
• velocity + acceleration: NO!
Adding Vectors – head to tail
method
1.
2.
3.
4.
5.
Start with a bold dot
Draw the longest vector first
Draw the next vector head to tail
Draw the resultant from the big dot to
the last arrow head.
Measure the resultant (graphically,
measured, or calculated).
Vectors – same axis
Vectors have magnitude and direction. They add or subtract
depending on their directions.
Parallel vectors are pretty simple:
50 m
+
50 m
50 m/s
+
100 m
=
50 m/s
=
0 m/s
What is the likely hood of
being found?
A camper in Yosemite park gets disoriented
while hiking. They know they have traveled
50 kilometers from the park entrance. They
are able to send a message to the park
ranger to say they are lost and have
traveled 50 kilometers. How easy will it be to
find the hiker?
Adding vectors – different
directions
A
A
C
B
A+B=C
B
What is the Pythagorean Theorem?
a +b = c
2
2
2
Pythagorean Theorem
a2 + b2 = c2
152 + 202 = c2
225 + 400 = c2
625 = c2
625 = c
2
25 = c
Practice –drawing vectors
 In

groups of five do the following:
Use the tip to tail method to draw, calculate the
resultant, and determine a direction for the
following vectors:
 Diagram
‘C’ from your worksheet (vector sizes are
24 cm and 12 cm)
 Diagram ‘H’ from your worksheet (vector sizes are
36 cm and 18 cm.
 Diagram ‘I’ from your worksheet (vector sizes are
20 cm and 20 cm)
Project Brainstorming
 Objective
describe a real world example of
how vectors are used

Brain storm ideas (examples: navigating, game
plays for a sport, etc.). You are not/should not
be limited to these idea.
 Record
your ideas for your scenario and
have it reviewed by me before proceeding.