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