PHYSICS 9/19/2011
VECTORS
Warmup: An airplane is flying north at
75 m/s. A tailwind of 25m/s kicks up (a
tailwind is coming from behind the
plane). How fast is the plane flying
relative to the ground?
With the same wind, how fast would the
plane be traveling relative to the ground
if he turned around and flew the
opposite direction?
Notes for your notebook—
words you’ll need to know
 Magnitude
 Vector
 Sine
 Scalar
 Cosine
 Resultant
 Tangent
 Projectile motion
 Right triangle
 Circular motion
 Pythagorean
 Centripetal
Theorem
 Hypotenuse
acceleration
 Frame of reference
OOOOh, Vectors are scary
 No, they aren’t. In fact, you already know
what a vector is.
 Vector is a quantity with:
 Magnitude
 Direction
Examples of vector quantities: displacement,
velocity, acceleration, force, momentum
Wait, isn’t that pretty much
everything?
 NO!
 For some quantities, there is no direction.
 Speed and distance are two we have already
discussed
 What are some others you can think of? Tell your
neighbor
 Some examples: time, work, energy
 These quantities can be added and subtracted
with a regular old four function calculator
Back to vector quantities
 For our airplane, we found the resultant




velocity by simply adding or subtracting.
This ONLY WORKS when vectors are
PARALLEL
What happens when vectors are not parallel?
When you add scalar quantities (numbers)
you get a “sum”
When you add vectors, you get a resultant
Representing vectors
 Your book uses boldface to represent a
vector, eg: v=25 m/s
 I will draw a little hat on top of it.
 We show magnitude and direction by
drawing arrows to represent vectors
 Direction is represented by an angle
 Magnitude is represented by the length of the
arrow
Adding Vectors graphically
Tip to tail method Put the “tip” of the first vector on the “tail” of
the second vector
 If you draw vectors to scale and perfectly,
then you can use a protractor and ruler to
measure the resultant vector
http://www.walterfendt.de/ph14e/resultant.htm
Practice vector equations
Practice tip to tail
Can you draw perfectly?
 Maybe
 For those of us who cannot, vee haf udder
vays
 Namely, we “resolve” the vector into its
“components,” add the components, then
turn it BACK into a vector using the
Pythagorean theorem.
Right Triangles—a review
Pythagorean Theorem
2
2
2
A +B =C
Cool website
 http://www.physicsclassroom.com/Class/vect
ors/U3l1b.cfm
Example—ON Warmup
 An archaeologist climbs the Great pyramid in
Giza, Egypt. If the pyramid’s height is 136m
and its width is 230m, what is the magnitude
and direction of the archaeologist’s
displacement while climbing from the
bottom of the pyramid to the top?
Resolving Vectors
on w/up
 Find the component velocities of a helicopter
traveling 95 km/hr at an angle of 35° to the
ground.
Break it down and add it up
While Dexter is on a camping trip with his boy
scout troop, the scout leader gives each boy a
compass and a map. Dexter's map contains
several sets of directions. For the two sets
below, draw and label the resultant (R). Then
use the Pythagorean theorem to determine
the magnitude of the resultant displacement
for each set of two directions.
 Dexter walked 50 meters at a direction of
225° and then walked 20 meters at a direction
of 315°.
 Dexter walked 60 meters at a direction of
135° and then walked 20 meters at a direction
of 45°.
In a classroom lab, a physics student walks
through the hallways making several small
displacements to result in a single overall
displacement. The listings on the next slide
show the individual displacements for
students A and B. Simplify the collection of
displacements into a pair of N-S and E-W
displacements. Then use Pythagorean
theorem to determine the overall
displacement.