Vectors

Adding Vectors

+ =

Resu

ltant

Adding Vectors

+ = Resultant

+ =Resultant

Adding Vectors (now with numbers!)

+ =4 m East 3 m North

4 m

3 mr = 5 m

Adding Vectors (now with numbers!)

+ =4 m East 3 m North

4 m

3 mr = 5 m

θ

Make sure your calculator is in DEGREES mode!!!!!!

Measuring AnglesMeasure ALL angles starting from the positive x-axis!

+y

II180-θ90-180o

I θ0-90o

III180+θ180-270o

IV360-θ270-360o

+x -x

-y

Vector Components

x-component

y-component

θ

Vectors are made up two components: x & y

Vector Components

x-component = rx

y-component = ry

θ

r

Adding Multiple Vectors

• Find x & y components of each vector• Add all x’s to get final x component• Add all y’s to get final y component• Pythagorean theorem• tan-1

Relative Velocity• If two objects are moving towards or away

from each other, depending on your reference point, the velocity may appear to be different (relative velocity)

Boat ProblemsTo measure “relative to shore”, measure the angle between the shore and the resultant

θ

θ