1. Vectors Unit 4

2. Objectives Draw vectors to scale Find the resultant from two vectors
Separate vectors into their components (x & y)
Add and subtract vectors algebraically
Relate vectors to the motion of objects

3. Grab a ruler please.

4. Review - Vector Quantities
A physical quantity that has both direction and magnitude
Displacement
Velocity
Acceleration
Force
A push or pull in a given direction

5. +90 m/s What is a vector? Velocity 20 km/h east
A vector is a graphical representation of vector quantity.
An arrow represents the magnitude and direction.
Velocity
+90 m/s
20 km/h east

6. + 100 pounds What is a vector? Force
A vector is a graphical representation of vector quantity.
An arrow represents the magnitude and direction.
Force
+ 100 pounds

7. - 9.81 m/s2 What is a vector? Acceleration
A vector is a graphical representation of vector quantity.
An arrow represents the magnitude and direction.
Acceleration
m/s2

8. Parts of a vectors
Magnitude (length)
Direction (arrowhead)

9. Rule #1 – Use a ruler when drawing vectors to scale.
Draw the magnitude using a ruler (choose a proper scale)
Add the arrowhead
Label the vector
Rule #1 – Use a ruler when drawing vectors to scale.

10. Drawing Vectors Scale 1 cm = 10 mi/h 40 mi/h East 25 mi/h West
57.5 mi/h North

11. Multiple Vectors Head to tail method Parallelogram Method
Each subsequent vector is drawn at the head of the last
Parallelogram Method
The tails of two vectors have the same origin (starting point)
Forces

12. Combining Vectors - Resultants
A resultant is the combination of 2 or more vectors
Head to tail method
Draw your resultant from the tail of the first to the head of the last

13. Combining Vectors – Resultants (cont.)
Parallelogram Method
Complete the parallelogram and draw a resultant from the 2 tails to the 2 heads.

14. Mathematically Combining Vectors
Vectors in the same direction
Sum the magnitudes
The direction remains the same
20 miles East
35 miles East
55 miles East

15. Mathematically Combining Vectors
Vectors in opposite directions
Subtract the magnitudes
Keep the direction that had the larger magnitude originally
20 miles East
35 miles West
15 miles West

16. Mathematically Combining Vectors
Vectors at right angles to each other
Use Pythagorean Theorem for the magnitude
a2 + b2 = c2
Use Trigonometry for the direction
25 miles NE
15 miles North
20 miles East

17. Breaking Down Vectors in Components
Vectors can be broken down into x and y components.
y-component
X-component

18. Breaking Down Vectors in Components
Vectors can be broken down into x and y components.
y-component
X-component

19. Breaking Down Vectors in Components
Use trigonometry to solve for the components mathematically
SOH CAH TOA
Hypotenuse
50 miles
Opposite
20°
Adjacent