1. Vectors

2. Scalars A scalar is a quantity that has magnitude only (no direction)
Examples of Scalar Quantities:
Distance
Area
Volume
Time
Mass

3. Vectors
A vector quantity is a quantity that has both magnitude and a direction in space (has both x and y components)
Examples of Vector Quantities:
Displacement
Velocity
Acceleration
Force
Weight

4. Magnitude and direction
20 m/s at 125o (if no direction is given, it is the
angle with horizontal)
40 N at 25o north of west

5. Direction
90 o North y + - +
0 o East x
West 180 o
360 o

6. To find x and y components given magnitude and direction
Use trig!!
Each vector is made up of an x component and a y component
To find the x component, multiply the magnitude by cos θ
To find the y component, multiply the magnitude by sin θ A
Asinθ θ
Acosθ

7. Example
Find the components of a vector with magnitude of 30 m/s at 40o

8. Example
Find the components of a vector with magnitude of 120N at 25o west of north

9. To find magnitude and direction given components
Magnitude can be found using the pythagorean theorem!!
Direction is found using trig!
If vector is not in 1st quadrant, you will need to change the answer your calculator gives you y θ x

10. Vector Addition
When you add vectors, the answer is called the resultant
To find the resultant, simply add the components

11. An airplane is flying 200m/s at 50o N of E
Wind velocity is 50 m/s due S.
What is the velocity of the plane? N 50
200 ? W E
VR = m/s @ ° S