VECTORS
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VECTORS. Recall that a vector has both:. Direction. Magnitude. The sum of two vectors is considered the resultant vector. +. Vector A. Vector B. A + B = R. Graphical Method. You must add vectors from head. head. to tail. tail. so. +. Vector B. Vector A. equals. Vector R.

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VECTORS

Recall that a vector has both:

  • Direction

  • Magnitude


The sum of two vectors is considered the resultant vector

+

Vector A

Vector B

A + B = R


Graphical Method

You must add vectors from head...

head

to tail...

tail

so...


+

Vector B

Vector A

equals

Vector R


For Example:

A man walks 275m due east then another 125 m due east. What is his resultant displacement?


A man walks 275m due east then another 125 m due east. What is his resultant displacement?

PART 1

PART 2

275 m

125 m

Using a ruler you measure from the beginning of part 1 to the end of part 2


RULER is his

A man walks 275m due east then another 125 m due east, what is his resultant displacement?

PART 1

PART 2

275m

125m


RULER is his

A man walks 275m due east then another 125 m due east. What is his resultant displacement?

275m

125m


RULER is his

=

RESULTANT

400m

275m

125m


RESULTANT: is his 400m East


A man walks 275m due east then another 125 m due is his west. What is his resultantdisplacement?


A man walks 275m due east then another 125 m due is his west. What is his resultant displacement?

PART 1

275 m


A man walks 275m due east then another 125 m due west. What is his resultant displacement?

PART 2

125 m

Using a ruler, measure from the beginning of part 1 to the end of part 2


RULER is his

A man walks 275m due east then another 125 m due west. What is his resultant displacement?


RULER is his

A man walks 275m due east then another 125 m due west. What is his resultant displacement?

275m

125m


RULER is his

=

RESULTANT

150m

275m

125m


RESULTANT: is his 150m East


A man walks 275m due east, then another 125 m due is his north. What is his resultantdisplacement?


A man walks 275m due east then another 125 m due north. What is his resultant displacement?

N

PART 2

125 m

PART 1

E

275 m


Using a ruler you measure from the beginning of part 1 to the end of part 2

125 m

PART 2

PART 1

275 m

E

N


RULER the end of part 2

E


RULER the end of part 2

N

E


302m the end of part 2

=

N

RESULTANT

E


Now we have the magnitude of the resultant vector we need a direction for the resultant vector

so…

We get our protractors out and measure the angle of the resultant vector


302m direction for the resultant vector

=

N

RESULTANT

24.4°

E


Resultant Vector direction for the resultant vector

302 m; 24.4° North of East


ANGLE NOTATION direction for the resultant vector

On the last one we wrote 40° “North of East”, b/c we were saying it went 40° North “from” East.

In your notebook try the following for practice


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° East of North


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° South of East


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° East of South


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° West of South


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° South of West


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° North of West


N direction for the resultant vector

W

E

S

30°


ANSWER: direction for the resultant vector30° West of North



What direction is a vector directed northeast or southwest1
What direction is a vector directed “northeast” or “southwest”?

  • By definition, “northeast”, “southeast”, “southwest”, and “northwest” are vectors directed at 45 degrees.


Not only can we add vectors “southwest”?graphically, we can also find the resultant mathematically…


When vectors are added at right angles to each other, the “southwest”?Pythagorean Theorem can be used to determine the magnitude of the resultant.

Trigonometric functions can be used to determine the direction.


A plane travels at 450 km/h due north with a wind blowing at 120 km/h due east. What is the resultant velocity of the plane?

120 km/h

450 km/h


120 km/h due east. What is the resultant velocity of the plane?

120 km/h

450 km/h

tan = 120/450

R = 466 km/h 15 east of north


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