Name:_________________ Physics 11 Date:______________

UNIT 5 Vectors

5.2 – Analytical Method of Vector Addition 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)

35º

12.3

14.8º

6.7 5.4º

8.79

40º

27.6

A B C D

Find the resultant vector for:

1) A + B 2) B + D + C 3) B - A

4) D + D 5) C - C 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