• Check in WS 1.• Then get out your notebook.

Vectors – “mathematical objects” (arrows) that have both

magnitude and direction.

–Example of vector quantities: • Displacement• Velocity• Acceleration

Note: all of these have DIRECTION and SIZE (magnitude).

Magnitude • the length of a vector (how big it is). • Ex: a velocity of -5m/s has a magnitude of 5m/s and a

direction to the left. • Mathematically it means the absolute value.

Scalars • quantities that are numerical, but have no

direction. • 5 kg (mass), 15 mL (volume)• 20 s (time), -20°C (temperature)• Speed, distance

How to Use a Protractor

• Review– Vectors vs. Scalars: what’s the difference?

• Discuss your results of randomizing the directions on WS 1 with your group members. Be prepared to share the group’s answers for questions 1-4.

• Each leg of the trip is a vector. It has a length and a direction.

• Putting together each leg of the trip is the same thing as adding vectors.

• No matter what order you use, you still get to your final destination.

• The order you add vectors doesn’t matter.

• Vector addition is commutative. The order you add them doesn’t matter!

• The sum of a bunch of vectors is called the resultant.

Graphically Adding Vectors• The order you add them doesn’t matter.• Connect the vectors “tip to tail.”– (Your next map instruction starts where the other

ended.)

• The resultant vector is a vector drawn from where you started to where you ended.– START POINT to END POINT

• Each group needs a whiteboard, an eraser, a black marker, and a color marker.

Example 1

+ = ?

Example 2

+ = ?+

WRONG

Example 2

+ = ?+

WRONG

Example 2

+ = ?+How do we report the direction of the resultant? An angle by itself is meaningless.

Reporting Angles from the x-axis

x

y

-x

-y

Positive Angles

Just like math class

Reporting Angles from the x-axis

x

y

-x

-y

Negative Angles

Just like math class

• If only a degree measurement is given, assume it’s measured from the x-axis, just like you do in math class.

Reporting Angles from Any Axis

E

N

W

S

N of E

E of N

W of N

N of W

S of W

W of

S E of SS of E

Reporting Angles from Any Axis

E

N

W

S

N of E

E of N

W of N

N of W

S of W

W of

S E of SS of E

Practice

Using a protractor, add the following vectors. Measure the magnitude and direction of the resultant vector.

{2.5 cm @ 30° S of E} + {3 cm @ 75°}

{2.5 cm @ 30° SoE} + {3 cm @ 75°}

{2.5 cm @ 30° S of E} + {3 cm @ 75°}

{2.5 cm @ 30° SoE} + {3 cm @ 75°}

R=3.2 cm @ 30°

{2.5 cm @ 30° SoE} + {3 cm @ 75°}

R=3.2 cm @ 60° E of N

{1 cm @ 0°} + {2 cm + 90°} + {3 cm @ 180°}

{1 cm @ 0°} + {2 cm + 90°} + {3 cm @ 180°}

{1 cm @ 0°} + {2 cm + 90°} + {3 cm @ 180°}

R=2.75 cm

135°45°

45°

• WS 2 for homework• Each table needs to have 4 protractors on it