Enduring Understanding: Modeling is widely
used to represent physical and kinematic
information.
Essential Question: What are the practical
applications of modeling physical and kinematic
information?
Vectors
Draw an arrow. How
long is it?
? cm
1 cm = 20 miles
Now, the original arrow
represents something else.
How might this be useful?
Vectors are scale model arrow
representations.
Vectors have magnitude (size) and
direction.
Magnitude without direction is
called a scalar.
Give examples of direction.
Direction
We will also continue to use (+)
and (-) to indicate direction.
Scalar
Vector
Distance
Ex. 25 Miles
Speed
Displacement
Ex. 25 Miles South
Velocity
Give an example of a speed and a velocity.
Mass
Weight Time
Force
Vector Addition
The resultant is one vector that
represents the addition of two or
more vectors.
What is the resultant
displacement if you add 2 m east
to 3 m east?
2 m east
+
3 m east
Resultant 5 m east
Head to Tail Vector Addition
Activity – Add the Vectors
• On paper: draw diagrams for the
addition of the following vectors:
A. 2 m east
B. 4 m north
C. 5 m west
• Add the vectors 3 different ways using
a scale of 1cm = 1m:
ABC, BAC, CBA
• Do you think it matters what order you
add the vectors together?
Draw a head to tail vector diagram
showing the addition of 10 m north
+ 5 m south. What is the resultant
displacement?
5 m south
10 m north
Resultant: 5 m north
What is the resultant of 3 m east + 4
m north?
4m
3m
Pythagorean
Theorem
What is the resultant magnitude of
3 m east + 4 m north?
The magnitude = 5 m
How about the direction?
We would have to use
trigonometry for this but we can
give an approximate direction of
northeast (NE).
Draw a to scale head to tail diagram
representing this problem.
What are some real world
applications of vector addition?
A boat heads west across a river at
10 m/s. The current pushes the boat
south at 5 m/s. What is the resultant
speed of the boat?
11.2 m/s
How far does the boat travel in 30 s?
336 m
A 40 N force acts to the east as
a 60 N force acts to the south.
What is the magnitude of the
resultant force?
72 N
Vector Representation of
Projectile Motion
A vector has magnitude and
direction.
For each ball, draw vectors to
represent the horizontal
component of the velocity.
For each ball, draw vectors to
represent the vertical component
of the velocity.
Try it for this one.
Even More Vector Practice
1) A person walks 5 m to the
south. They stop for a rest. They
then travel 20 m farther to the
south. What was their resultant
displacement?
25 m south
2) Galileo is riding a bicycle and
is pedaling at 8 m/s to the west.
A 2 m/s wind is pushing to the
east. What is the resultant
velocity of Galileo and his
bicycle?
6 m/s west
3) A hiker travels 300 m west,
stops, checks a map and then
travels 700 m north. How far is
the hiker from their starting
point?
762 m
4) A boater drives a motorboat
out in the bay. The boat has a
speed 40 m/s directed west but
a current pushes it south at
10 m/s. What is the resultant
speed of the boat?
41.2 m/s
5) How long will it take the boat
to travel a distance of 2500 m?
60.7 s
6) A person walks 40 m east,
20 m south, 10 m west and
40 m north. How far are they
from their starting point?
36 m