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Phy 2053 Announcements
Phy 2053 Chapter 3
Vectors, and Motion in 2D
Thursday, Sept. 10, 2008—Gary Ihas
What to do? Zero v at the Top
Δ
x
2
v
v
2
0
2
a
+
=
v = 0
Throw ball up initial velocity nonzero and positive
Instantaneous velocity = 0 at maximum height
=0
Δ
x
x
∆
Can be given
v
0
and ask for
OR vice versa
Vectors let us keep track of our way in any number of dimensions
by carrying all the numberscomponentswe need in one symbol
square6
Here is a vector that shows
us going at an angle
Θ
with
the x axis
square6
It is useful to use
rectangular components
to manipulate vectors
square6
These are the projections
of the vector along the x
and yaxes
A
x
and
A
y
A
x
and
A
y
are scalars
Vector
Components
square6
The xcomponent of a vector
is the projection along the xaxis
cos
A A
θ
=
x
x
θ
=
uur
ur
cos
A
A
x
square4
The ycomponent of a vector is the
projection along the yaxis
sin
y
A A
θ
=
y
θ
=
uur
ur
sin
A
A
y
These equations are valid
only if
θ
is
measured with respect to the xaxis
x
y
=
+
r
r
r
A
A
A
Then,
Graphically Adding Vectors
square6
When you add vectors, just put
the tail of one on the head on
the next…
square6
The resultant
is drawn from
the origin of the first vector to
the end of the last
vectorVectors obey the
commutative law of addition
The order in which the vectors
are added doesn’t affect the
result
Note that vectors are
unchanged by being moved
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 Fall '06
 Buchler
 Physics, Acceleration, Projectile Motion, Velocity

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