1. Vectors

3. Scalar Terms ( Magnitude only)
Magnitude=quantitave measure or in simple terms, a number.
Time
Distance
Speed
Mass

4. Vector Terms (Magnitude and Direction) Displacement Velocity
Acceleration

5. Adding Vectors Vectors are represented by arrows
The size of the vector tells you about the amount of the quantity
Always add head to tail
Resultant- the vector that represents the sum of two or more vectors

6. Adding Vectors 6m 1m Now add from head to tail We add 6m +1m=7m 5m 2m
Now we add from head to tail
The resultant vector is 5m-2m=3m

8. At an angle
                                                                                            

11. To find components Hypotenuse Opposite Adjacent
To find components, you must use trigonometric functions
Hypotenuse
Opposite ø
Adjacent

12. Trig functions Θ is the angle between the vector and the x axis
sin Θ = _opposite_
hypotenuse
cos Θ = _adjacent_
tan Θ = _opposite_
adjacent

13. Steps for finding the components
Draw a picture (arrowheads, original vector & components)
Choose a trig function
Use algebra to solve for the desired variable & plug in
Calculator in degrees!
Check with Pythagorean theorem

14. Example
                                                      

15. X component cos Θ = _adjacent_ hypotenuse cos 35 = _adjacent_ 316
259 N = adjacent

16. Y component sin Θ = _opposite_ hypotenuse sin 35 = _opposite_ 316

17. How to find components when you add two vectors
Find the x and y component for both vectors
Add up the x components
Add up the y components
Draw a new set of vectors
Use Pythagorean theorem to get the magnitude of the resultant vector
Use arctangent to get the angle of the new vector

18. To find the angle of the resultant vector
Use arctangent function:
Θ = tan-1 (opp/adj)
Θ = tan-1 (30.2/9.1)
Θ = tan-1 (3.3)
Θ = 73.1°

19. Formulas
a2 + b2 = c2
R2 = a2 + b2 - 2ab(cosθ)
SOH
CAH
TOA