
Objectives 
Essential Question:
Is 1+ 1 = 2 always true ? 
Vector Addition Basics

State the relationship between a force's direction to
the resulting acceleration's direction.

State the relationship of a velocity's direction
to the resulting displacement's direction.

Sketch 2 ways to graphically add vectors.
 headtotail or heal to toe
 parallelogram

Define vector components.

Given vector components find the resultant vector
and its angle.

Given a vector find its components.
Homefun: Questions 110 p.64, Read
Chap. 3; Serway
Relevance: Vector addition makes it
possible to analyze complex motion in 3 dimensions. These motions
include everything from athletic activities to planetary motions.
Anyone who eventually wants to pilot an aircraft or sailboat needs to
have a basic understanding of vectors. 

Activities 
 Lesson 1
 Key Concepts: 1)
certain types of vectors always go in the same direction. 2) Vectors
can be added graphically. 3) Vectors can be broken into components.
 Purpose: Add
vectors.
Interactive Discussion:
Objectives. Which types vectors always go the same direction?
How are two vectors added in one dimension?
Practice with components
In Class Problem Solving:
Vector Addition
 Erie Canal Problem
 Airplane Problems
Etchasketch
Demo: Add vectors with the etchasketch. Show
components and how they look when added together.
Interactive Discussion:
Objectives Find components and angles graphically. Derive
mathematical formulas for components. Find components
mathematically.
Resources/Materials: Protractors,
etch a sketch
Formative Assessment:
Group and individual problem solving on white boards. 

Essential Question:
What is the fastest way to swim
across a raging river? 
Using Vector Components

State the relationship between the magnitudes of
vector components.

Solve problems involving adding or subtracting 2 vector
components.
 Swimmer problemsRunning Bear

Airplane problems
Homefun: problems 7, 17, 23, p.65
 70; Serway
 Metacognition Problem Solving Questions:
 When adding two vector components (from different dimensions)
:
 Is
the resultant's
magnitude less than the
sum of the two magnitudes?
 Is the resultant's magnitude greater
than the smallest component?
The resultant is always less than the sum of
the components magnitudes but always greater than the smallest components
magnitude.
Relevance: Thinking in terms of
vector components helps simplify vector addition.

 Lesson
2
 Key Concept: The
x and y components are independent
 Purpose: Solve vector
problems involving components.


Interactive Discussion:
Objectives. Introduce the running bear problem . In Class Problem Solving:
Vector problems

Add two components.

Given a vector,
convert it to components.
 Running Bear
Formative
Assessment: Group and individual problem solving on white boards. 

Essential Question:
How can an airplane's speed be
measured? 
Special Vector Notation
 Use unit vectors (i, j, k).
 Add
multiple vectors together using the three step component method.
Homefun: problems 47, 49, 53, 61, p.65
 70; Serway
Relevance: Anyone who eventually
wants to pilot an aircraft or sailboat needs to have a basic understanding
of vectors. Summative
Assessment: Unit Exam objectives 110. 

 Lesson 3
 Key Concept: Multiple vectors
at various angles can be added using components
 Purpose: Add multiple vectors.
Interactive Discussion:
Objectives. Discuss i, j, k unit vector notation and addition. Show three step method
In Class Problem Solving:
Vector problems
 Running Bear (continued)
 Airplane Problems  ground speed
 Three vector addition
Formative Assessment:
Group and individual problem solving on white boards. 
 Summative Assessment: MiniLab
Physics Investigation (Requires only Purpose,
data, and conclusion)

Title 
Analysis of Wind Tunnel Fan's Output 
Purpose 
Measure the ACFM output of a wind tunnel's fan and compare
it to the factory's specification. 
Overview 
 Divide the fan into annular rings with the same width
(about 45 inches wide).
 Measure the air flow velocity in the annular rings at 4
positionstop, bottom, right side, left sideand average the
measurements.
 Multiply the average air flow velocity for each of the
rings by the area of the ring to obtain the volume flow rate
for each ring.
 Sum up the volume flow rate for each ring. This gives an
estimate of the total volume flow rate for the fan.
 Convert to the correct units.
Note: according to the factory, the fan's volume flow rate =
13,000 ACFM 
Data,
Calculations 
Calculate a % difference between the measured and factory
specification of volume flow rate. 
Questions,
Conclusions 
What would happen to the accuracy of the measured value if
it was calculated using many more rings. (Assume the velocity
measurements in any sized ring is perfect) Why is the velocity
in the outer ring higher than the inner rings? 
Resources/Materials: 
Wind tunnel with fan, air velocity probe, 
