pptg101213_addition of vector by component method_gallego

7/31/2019 PPTG101213_Addition of Vector by Component Method_GALLEGO

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The Right Triangle |Component of vectors |Resultant vectors by component method

28 July 2012 REDG 2011 1


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28 July 2012 REDG 2011 2

The Right Triangle

(c)

(b)

(a)

2 2 2

2 2

c = a +b

c = a +b

Solve for a and b. 2 2 2

2 2 2

a = c -b

b = c -a


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28 July 2012 REDG 2011 3

The Right Triangle

hypotenuse

adjacent

opposite


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28 July 2012 REDG 2011 4

The Right Triangle

hypotenuse

opposite

adjacent


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28 July 2012 REDG 2011 5

The Right Triangle

The opposite alwaysfaces opposite to the

reference angel


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28 July 2012 REDG 2011 6

The Right Triangle

Identify the opposite, adjacent, and

hypotenuse in each right triangle below.

x

2 3

54

1y z

b

a

cx

y

z

c

ab

q

ps


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28 July 2012 REDG 2011 7

Trigonometric Functions

oppositesin=

hypotenuse

adjacentcos=

hypotenuse

oppositetan=

adjacent


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28 July 2012 REDG 2011 8

The Right Triangle

Write the equations to get the values of the

unknown side (represented by letters in redcolor).

x

1y z 2

b

a

c 3x

y

z

4

c

ab

5

q

ps


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28 July 2012 REDG 2011 9

Resultant Vectors


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28 July 2012 REDG 2011 10

Resultant Vectors

How do we determine for the x-component? What

about for the y-component?

Hint:

Identify the adjacent

and opposite


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28 July 2012 REDG 2011 11

Resultant Vectors

From the given x-component and y-component, how do

you get the resultant vector?

Hint:

The resultant vector is

the hypotenuse of thetriangle.


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28 July 2012 REDG 2011 12

Resultant Vectors

From the given x-component and y-component, how do

you determine the angle?


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28 July 2012 REDG 2011 13

Resultant Vectors

Given the following vectors, determine the magnitude of

the resultant.

2 2

R

2 2

d = x +y

= 300 +200

= 130000

=360m


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28 July 2012 REDG 2011 14

Resultant Vectors

Given the following vectors, determine the direction of

the resultant vector.

-1

-1

O

y=tan

x

200=tan

300

=33.7


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28 July 2012 REDG 2011 15

Resultant Vectors

Given the following vectors, determine the direction of

the resultant vector.


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28 July 2012 REDG 2011 16

Component Vectors


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28 July 2012 REDG 2011 17

Component Vectors

Describe the x- and y- components of each vector.


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28 July 2012 REDG 2011 18

Component Vectors

Find the component of this vector


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28 July 2012 REDG 2011 19

Component Vectors

Find the component of this vector


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28 July 2012 REDG 2011 20

Component Vectors

Find the component of these vectors


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28 July 2012 REDG 2011 21

Resultant Vectors

A flock of birds follows the same migratory

pattern every year. Biologists noted that

they originate from Japan and flies 2500 km60o S of W to Taiwan for a stopover. The

flock will then turn 400 E of S and cover a

distance of 1500 km towards the BatanesIslands in the Philippines. Identify the

components of each vector.

Determine the x- and y- components of each of

the vectors in the problem below.


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28 July 2012 REDG 2011 22

Resultant Vectors

A flock of birds follows the same

migratory pattern every year. Biologists

noted that they originate from Japan andflies 2500 km 60o S of W to Taiwan for a

stopover. The flock will then turn 400 E of

S and cover a distance of 1500 km

towards the Batanes Islands in the

Philippines. How far are they from Japan?

Represent the vectors in the problem below and

determine the resultant vector.


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28 July 2012 REDG 2011 23

Resultant Vectors

x-component y-component

d1 -1250 -2165

d2 964 -1149


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28 July 2012 REDG 2011 24

Resultant Vectors

2 2

R

2 2

d = x + y

= -286 + -3314

= 11 064 392

=3326 m

-1

-1

-1

O

x=tan

y

286=tan

3314=tan 0.086300543

=4.93


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28 July 2012 REDG 2011 25

Resultant Vectors

A sailboat is cruising up the Amazon

River. Its sails embraces a 40 km/hr wind

directed at 60o W of N and another windthat is moving at 35 km/hr towards the

West. If the downstream current is

moving at 10 km/hr directed at 20o East

of South, what is the resultant velocity of

the ship.

Represent the vectors in the problem below and

determine the resultant vector.


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28 July 2012 REDG 2011 26

Most explanation and examples in this presentation are basedof the lesson presentation ofThe Physics Classroom &

Conceptual Physics. The clip arts used were taken from

different sites that I thought are free to use. This is for

classroom use only.

pptg101213_addition of vector by component method_gallego

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