Physics 11
Date:______________
UNIT 5 Vectors
5.2 – Analytical Method of Vector Addition
Name:_________________
Vector addition is dealt in three conceptually equivalent ways:
1. graphical methods
2. analytical methods
3. algebraic methods
Recall the tools needed to solve vector problems:
Pythagorean Theorem
Primary Trig Ratios
Vector addition: graphical method
If two vectors are represented by two sides of a triangle in sequence, then third closing side of the triangle, in the opposite
direction of the sequence, represents the sum (or resultant) of the two vectors in both magnitude and direction.
Vector addition: Analytical method
We shall analyze vector addition in the form of triangle law to obtain the magnitude of the sum of the two vectors. Let P
and Q be the two vectors to be added, which make an angle θ with each other. We arrange the vectors in such a manner that
two adjacent sides OA and AB of the triangle OAB, represent two vectors P and Q respectively as shown in the figure .
Angle Directions – using an x – y plane we define angle directions in the following way:
Example: An airplane flying toward 0 at 90.0 km/h is being blown toward 90 at 50.0 km/h. What
is the resultant velocity of the plane?
Components of Vectors
We have seen that when we have 2 or more vectors acting in different directions a single vector results
called the ____________________.
Example:
We will now start with a single vector and determine the 2 vectors that produced it. These 2 vectors
are the ______________________ of the vector. The vector F has a _______________ component,
and a _____________ component.
How can we find ________ and ________? Using Trig!
Example:
Example: A wind with a velocity of 40.0 km/h blows toward 30.0?
(a) What is the component of the wind’s velocity toward 90?
(b) What is the component of the wind’s velocity toward 0?
Example: A wagon is being pulled by a rope that makes a 25O angle with the ground. The person is
pulling with a force of 103 N along the rope. Determine the horizontal and vertical components of the
vector.
Example: A plane flies 34 km [N30OW] and after a brief stopover flies 58 km [N40OE]. Determine
the plane's displacement.
Homework/Class work: 1. Read pgs 113 – 118
2. Do pgs 115 – 116 #7 – 9 and pg 118 #11 – 14
Name:____________________
Block: ___________
5.2 – Assignment #2
Vector Addition and Subtraction - Graphically & Analytically
Part 1 - Graphical Method
Given the 6 different graphed vectors labeled A through F on the back of this page, perform the
following vector additions. Place them on the graph paper where you like, but be sure to label them
properly. Find the resultant vector for:
1)
A+B
2)
A+C+F
3)
B+D-E+F
4)
A+E+D+E
5)
F+C-A
6)
D-E+F-A
Part 2 - Analytical Method
Given the following vectors, labeled A through D. perform the following problems. Be sure to resolve
the vector into components when adding them. (Note, the vectors below have no associated unit...
imagine you’re adding displacements, or forces, or velocities... it is not really important)
27.6
8.79
12.3
14.8º
35º
A
B
40º
5.4º
6.7
C
D
Find the resultant vector for:
1)
A+B
2)
B+D+C
4)
D+D
5)
C-C
3)
B-A
6)
D + C - (A - B)
A
B
C
D
E
F
_
Note: one square in the graphs above is scaled to equal one square below