Blue Bow
• A car is travelling at 30 m/s. The
driver sees a deer about 100 m ahead
and hits the brakes and begins to slow
down at a rate of 5 m/s/s. How fast is
the car going after 60 m?
DIRECTION
• Make a compass sign on all your
problems!
• A rock is dropped from an airplane.
– What direction is the acceleration?
– What is the initial velocity in the y-direction
(up and down)?
– What direction is the final velocity?
– What direction is the displacement?
Homework
Today’s Objectives
• Take a closer look at vectors so that we can
describe their size and direction pictorially.
This will help us to make sense of more
complicated problems.
• We will use trigonometry to break vectors
down into their “components”.
Homework
• Web Assign
• If you are having difficulty with kinematics,
use the weekend to watch some Khan
videos.
• Feel free to watch Khan videos on vectors
as well.
• <iframe
src="http://phet.colorado.edu/sims/projectil
e-motion/projectile-motion_en.html"
width="800" height="600"></iframe>
Pointing the Way
Vectors
Representing Vectors
• Vectors on paper are simply arrows
– Direction represented by the way the ARROW POINTS
– Magnitude represented by the ARROW LENGTH
• Examples of Vectors
– Displacement
– Velocity
– Acceleration
Angular Systems
Compass
Reference
Point
Vector
System
Uses
Usesangles
due EAST
measured
as thefrom
0 degree
various
reference,
compass
all other
points
angles
to reference
are measured
vectorfrom
direction
that point
20 meters
20 meters
at 10° at
south
190°of west
34 meters
34 meters
at 42° east
at 48°
of north
90°
N
180°
W
E
0°
S
270°
Changing Systems
• What is the reference vector angle for a
vector that points 50 degrees east of south?
270° + 50° = 320°
50°
• What is the reference vector angle for a
vector that points 20 degrees north of east?
20°
20°
Practice
What we can DO with vectors
• ADD/SUBTRACT with a vector
– To produce a NEW VECTOR
• MULTIPLY/DIVIDE by a vector or a scalar
– To produce a NEW VECTOR or SCALAR
Adding Vectors Graphically
Tip to Tail Method !
Adding Vectors Algebraically
• Vectors can be broken into COMPONENTS
• X-Y system of components
• AX = A cos θ
• AY = A sin θ
– Example
• vi = 5.0 m/s at 30°
– vix = 5.0 m/s (cos 30°) = 4.33 m/s
– viy = 5.0 m/s (sin 30°) = 3.21 m/s
Adding with Components
• Vectors can be added together by adding
their COMPONENTS
• Results are used to find
– RESULTANT MAGNITUDE
– RESULTANT DIRECTION
Practice