vector addition
DESCRIPTION
Vector Addition. Adding Multiple Vectors by Drawing. To add vectors you place the base of the second vector on the tip of the first vector You make a path out of the arrows like you’re drawing a treasure map - PowerPoint PPT PresentationTRANSCRIPT
Vector Addition
Adding Multiple Vectors by Drawing
To add vectors you place the base of the second vector on the tip of the first vector
You make a path out of the arrows like you’re drawing a treasure map
The answer vector (called the resultant) is the vector that connects the start of the path to the end of the path.
Measure the resultant with a ruler to find the magnitude.
Add These Vectors by Drawing
3 cm @ 90° + 6 cm @ 0° = ?
resultant (answer vector)
Tip-to-Tail
This method of adding vectors is called the “Tip-to-tail method” since you put the tail of the second vector on the tip of the first vector
resultant (answer vector)
Adding Vectors Mathematically When adding perpendicular vectors
you use the Pythagorean Theorem
a
bc
Finding the Direction
When adding vectors by drawing you use a protractor and measure the angle of the resultant.
When adding vectors mathematically you use Trigonometry to find the direction of the resultant.
Trig Functions
Sine (sin) Cosine (cos) Tangent (tan) Each function uses two sides of a
right triangle The angle we are using is labeled with
the Greek letter “theta” or “θ”
SOH-CAH-TOA
θ
hypotenuse
op
posi
te
adjacent
Angles
Angles are measured from the +x-axis
Quadrant 1: 0°-90°Quadrant 2: 90°-180°
Quadrant 3: 180°-270° Quadrant 4: 270°-360°
Your calculator will give you the angle
to the closest part of the x-axis. You need to add or subtract to adjust the angle to the ranges shown.
y
x
Example: MagnitudeA hiker hikes 22 km East, then 11 km North. Determine the magnitude and direction of the hiker’s displacement.
θ
22 km
11 kmresultant
Example: DirectionA hiker hikes 11 km East, then 22 km North. Determine the magnitude and direction of the hiker’s displacement.
θ
22 km
11 kmresultant
Your calculator must be in degrees mode!