1. Chapter 3

2. Objectives Express scalar and vector quantities
Understand the relationship between
scalar and vector quantities
Calculate and manipulate vector
components for right triangles

3. Scalar – a quantity that has a magnitude (number), but no direction
ex. Volume, mass
3 kg
Vector - a quantity that has a magnitude (number) and direction
ex. velocity, displacement, acceleration
3 m/s south

4. Vectors can be added graphically
Resultant – answer
found by adding
vectors

5. Vectors can be added graphically
Vectors can be moved parallel to themselves in a diagram
Vectors can be added in any order
To subtract a vector, add its opposite

6. Determining resultant magnitude
Pythagorean Theorem for right triangles
d2 = x2 + y2
(Length of hypotenuse)2 = (length of one leg)2 + (length of the other leg)2

7. Determining resultant direction
The angle (θ) of the resultant is the direction of the resultant

8. Determining resultant direction
To find just the angle, use the inverse of the tangent function

9. Resolving vectors into components
Components - the horizontal and vertical parts that add up to the resultant
By breaking a single vector into its components, the motion can be more easily described (ie. north to south)

10. Two dimensional Motion
Vector operations uses the “x” and “y” axis.
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12. Vector components
To find the x and y components, use the sine and cosine functions
Components can be positive or negative numbers with units
Units for the components will be the same as the units of the hypotenuse

13. Vector Components Θ d y x All right triangles must have 4 things:
d, Θ, x, y
You will solve for what is missing. Θ d y x

14. Vector components opposite leg = hypotenuse (sin Θ)
adjacent leg = hypotenuse (cos Θ)

16. Ex. Find the component velocities of a helicopter traveling 95 km/h at an angle of 35o to the ground.

17. Remember when you solve for the displacement you are looking for the magnitude (d) and the direction (Θ)