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Recall that a vector has both: •Direction •Magnitude

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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. - PowerPoint PPT Presentation

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Page 1: Recall that a vector has both:

Recall that a vector has both:

•Direction

•Magnitude

Page 2: Recall that a vector has both:

The sum of two vectors is considered the resultant vector

Vector A Vector B

A + B = R

+

Page 3: Recall that a vector has both:

You must add vectors from head...

head

to tail...

tail

so...

Graphical Method

Page 4: Recall that a vector has both:

Vector A Vector B+

equals

Vector R

Page 5: Recall that a vector has both:

For Example:

A man walks 275m due east then another 125 m due east. What is

his resultant displacement?

Page 6: Recall that a vector has both:

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

PART 1

275 m

PART 2

125 m

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

end of part 2

Page 7: Recall that a vector has both:

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

PART 1

275m

PART 2

125mRULER

Page 8: Recall that a vector has both:

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

275m 125mRULER

Page 9: Recall that a vector has both:

275m 125mRULER

RESULTANT = 400m

Page 10: Recall that a vector has both:

RESULTANT: 400m East

Page 11: Recall that a vector has both:

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

his resultant displacement?

Page 12: Recall that a vector has both:

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

PART 1

275 m

Page 13: Recall that a vector has both:

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

Page 14: Recall that a vector has both:

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

RULER

Page 15: Recall that a vector has both:

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

275m 125mRULER

Page 16: Recall that a vector has both:

275m 125mRULER

RESULTANT = 150m

Page 17: Recall that a vector has both:

RESULTANT: 150m East

Page 18: Recall that a vector has both:

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

his resultant displacement?

Page 19: Recall that a vector has both:

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

PA

RT

2PART 1

275 m12

5 m

E

N

Page 20: Recall that a vector has both:

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

PA

RT

2PART 1

275 m12

5 m

E

N

Page 21: Recall that a vector has both:

RULER

E

Page 22: Recall that a vector has both:

E

NRULER

Page 23: Recall that a vector has both:

E

N

RESULTANT=

302m

Page 24: Recall that a vector has both:

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

Page 25: Recall that a vector has both:

E

N

RESULTANT=

302m

24.4°

Page 26: Recall that a vector has both:

Resultant Vector

302 m; 24.4° North of East

Page 27: Recall that a vector has both:

ANGLE NOTATION

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

Page 28: Recall that a vector has both:

E

N

S

W

30°

Page 29: Recall that a vector has both:

ANSWER: 30° East of North

E

N

S

W

30°

Page 30: Recall that a vector has both:

E

N

S

W30°

Page 31: Recall that a vector has both:

ANSWER: 30° South of East

E

N

S

W

30°

Page 32: Recall that a vector has both:

E

N

S

W

30°

Page 33: Recall that a vector has both:

ANSWER: 30° East of South

E

N

S

W

30°

Page 34: Recall that a vector has both:

E

N

S

W

30°

Page 35: Recall that a vector has both:

ANSWER: 30° West of South

E

N

S

W

30°

Page 36: Recall that a vector has both:

E

N

S

W30°

Page 37: Recall that a vector has both:

ANSWER: 30° South of West

E

N

S

W30°

Page 38: Recall that a vector has both:

E

N

S

W 30°

Page 39: Recall that a vector has both:

ANSWER: 30° North of West

E

N

S

W 30°

Page 40: Recall that a vector has both:

E

N

S

W

30°

Page 41: Recall that a vector has both:

ANSWER: 30° West of North

E

N

S

W

30°

Page 42: Recall that a vector has both:

What direction is a vector directed “northeast” or

“southwest”?

Page 43: Recall that a vector has both:

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

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

Page 44: Recall that a vector has both:

Not only can we add vectors graphically, we can also find the resultant mathematically…

Page 45: Recall that a vector has both:

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

Trigonometric functions can be used to determine the direction.

Page 46: Recall that a vector has both:

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?

450 km/h

120 km/h

Page 47: Recall that a vector has both:

450 km/h

120 km/h

22 120450 R

tan = 120/450

R = 466 km/h 15 east of north


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