Do you remember any trig?? When you are finished with the Exam, see if

you can solve these problems…..

1) Determine the value of the missing side.2) Determine the value of the angle.

3) Determine the value of the angle.

5.6

12.4

?8.5

4.2

??

Vectors and Scalars

Honors Physics

Scalar Vector Quantity of Magnitude

Ex: Speed Distance Volume Mass Time

Quantity of Magnitude and Direction

Ex: Velocity Acceleration Displacement

SymbolsSymbols in

BookOn Board

VectorBold Faced

ScalarItalics

Example Problem An airplane trip involves three legs with two

stopovers. The first leg is due east for 620 km; the second leg is 440 km at 45° south of east and the third leg is 550 km at 53° south of west. What is the plane’s total displacement?

Vector Diagram Way to organize information

Uses an arrow Direction Length of Arrow (Magnitude)

Q: Which vector represents the faster car?

1) Adding Vectors Add head to tail

Example: A person walks 8 km east

one day and then 6 km east, what is the person’s displacement from the origin?

8 km

6 km

Resultant = 14 km

2) Subtracting Vectors Subtract head to tail

Example: A plane is traveling 180

km/hr east and it experiences a headwind 50 km/hr west.

How fast can the plane actually go?

180 km/hr

50 km/hrResultant = 130 km/hr

3) Adding Perpendicular Vectors Can we use simple algebra if the person walks

4 km East and 3 km north?

4 km

3 kmResulta

nt

Pythagorean Theorem

a

Resulta

nt b

Vectors can be added in any order Regardless of path, the resultant vector will

have the same magnitude and direction Vectors can be moved parallel to

themselves in a vector diagram.

Example Problem #2 Emily tosses the baseball 13 m west across

the field to Jessica, who then throws the ball 24 m south to Melissa at home plate. What is the ball’s total displacement as it travels between Emily and Melissa?

Adding Vectors by Components

Resolving Component Vectors If the vector lines in a particular plane….It can

be expressed as the sum of the component vectors.

The horizontal and vertical vectors that add up to make the resultant vector are called components. Vector A

x- component

y- component

x- component

Vector B

y- component

Practice Problem #1 An archaeologist climbs the great pyramid of Giza, Egypt. If

the archaeologists travels178.1 m in a direction of 49.78° N of E, what is the magnitude of the pyramid’s height and its width?

A truck drives up a hill in a direction of 25° north of west. If the truck has a constant speed of 30 m/s, what are the x and y components of the truck’s velocity?

Practice Problem #2

Bell Ringer October 31st 20131. A trick-or-treater travels 130 m west down the street to

trick-or-treat their next house on Halloween night. Once they reach the edge of the house’s driveway they travel 26 m north to the house’s door.

a) Sketch a vector diagram representing the motion of the trick-or-treater.

b) What is the trick-or-treater’s total displacement as it travels down the street and up the driveway?

Bell Ringer November 1, 2013 A plane travels northeastward from an angle

of 35 degrees above the positive x-axis at a velocity of 95 km/hr. Determine the magnitude and direction of the x and y components of the plane’s velocity.

35°

v = 9

5

km/h

r

Day 2 Adding Multiple Vectors

Adding multiple vectors…. A busy postal worker delivering mail travels

25 m east to their first house then turns north and heads 43 m. They then travel 10 m west and finally travel 21 m north. What is the total displacement of the postal worker.

A = 25 m

B = 43 m

C = 10 m

D = 21 mVector Horizontal Vertical

A

B

C

D

R

Practice Problem #1 A dog searching for a bone walks 8 m south,

then 4.8 m east, then 2 m south and then finally10.2 m west. Determine the dog’s resultant displacement vector.

Vector Horizontal Vertical

A

B

C

D

R

Adding Non-Perpendicular Vectors A student jumps on a skateboard and travels

30 m east. He then turns sharply at an angle of 45° north of east and travels 70 m. Determine the resultant displacement of the skateboarder.

70 m

30 m45°

Vector Horizontal

Vertical

A

B

R

Practice Problem #2 A plane takes off at a 14˚ angle with the

horizon and travels 56 km. It then turns at an angle of 38˚ from the horizon and travels 84 km. Determine the resultant displacement of the plane.

56 km

84 km

14˚

38˚

Vector Horizontal

Vertical

A

B

R