Addition of Vectors

Topics: Hypotenuse, Right triangle, Addition Pages: 8 (777 words) Published: June 25, 2013
The Right Triangle |Component of vectors |Resultant vectors by component method

28 July 2012

REDG 2011

1

The Right Triangle (c) (a)

(b)
c = a +b
2 2 2 2 2

Solve for a and b.

a2 = c2 -b2 b2 = c2 -a2

c = a +b
28 July 2012

REDG 2011

2

The Right Triangle

hypotenuse opposite


adjacent
28 July 2012 REDG 2011 3

The Right Triangle

adjacent



hypotenuse

opposite
28 July 2012 REDG 2011 4

The Right Triangle

The opposite always faces opposite to the reference angel 

28 July 2012

REDG 2011

5

The Right Triangle
Identify the opposite, adjacent, and hypotenuse in each right triangle below.

 z y 1 x  a
28 July 2012

a  2 b b 4 c
REDG 2011

y c x p  5 s q
6

3



z

Trigonometric Functions
opposite sinθ= hypotenuse adjacent cosθ= hypotenuse opposite tanθ= adjacent

28 July 2012

REDG 2011

7

The Right Triangle
Write the equations to get the values of the unknown side (represented by letters in red color).

 z y 1 x  a
28 July 2012

a  2 b b 4 c
REDG 2011

y c x p  5 s q
8

3



z

Resultant Vectors

28 July 2012

REDG 2011

9

Resultant Vectors
Hint: Identify the adjacent and opposite

How do we determine for the x-component? What about for the y-component? 28 July 2012 REDG 2011 10

Resultant Vectors
Hint: The resultant vector is the hypotenuse of the triangle.

From the given x-component and y-component, how do you get the resultant vector? 28 July 2012 REDG 2011 11

Resultant Vectors

From the given x-component and y-component, how do you determine the angle? 28 July 2012 REDG 2011 12

Resultant Vectors
d R = x 2 +y 2 = 300 2 +200 2 = 130000 =360m

Given the following vectors, determine the magnitude of the resultant. 28 July 2012 REDG 2011 13

Resultant Vectors
y  =tan   x -1  200  =tan  300    -1

=33.7O

Given the following vectors, determine the direction of the resultant vector. 28 July 2012 REDG 2011 14

Resultant Vectors

Given the following vectors, determine the direction of the resultant vector. 28 July 2012 REDG 2011 15

Component Vectors

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16

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

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17

Component Vectors
Find the component of this vector

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18

Component Vectors
Find the component of this vector

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19

Component Vectors
Find the component of these vectors

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20

Resultant Vectors Determine the x- and y- components of each of the vectors in the problem below.

A flock of birds follows the same migratory pattern every year. Biologists noted that they originate from Japan and flies 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. Identify the components of each vector. 28 July 2012 REDG 2011 21

Resultant Vectors Represent the vectors in the problem below and determine the resultant vector.

A flock of birds follows the same migratory pattern every year. Biologists noted that they originate from Japan and flies 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? 28 July 2012 REDG 2011 22

Resultant Vectors

x-component y-component d1 -1250 -2165 d2 964 -1149 -286 -3314  28 July 2012 REDG 2011 23

Resultant Vectors

dR = =

x + y
2 2

2 2

  =tan   
-1

x   y  

 -286  +  -3314 

= 11 064 392 =3326 m

 286  =tan -1    3314  =tan -10.086300543 =4.93O REDG 2011 24

28 July 2012

Resultant Vectors Represent the vectors in the problem below and determine the resultant vector.

A sailboat is cruising up the Amazon River. Its sails...
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