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Chapter 3
Projectile
Motion
3.1 Vector and Scalar Quantities
VECTOR QUANTITIES –
quantities that have
magnitude and direction
EX: force and velocity
3.1 Vector and Scalar
Quantities
SCALAR QUANTITIES –
quantities that have
magnitude, but no direction
EX: mass, volume, time
MAGNITUDE – strength of
something
“how much?”
DIRECTION –
“which way?”
3.2 Vectors
vector – represented by an
arrow whose length is the
magnitude of a physical
entity and whose
orientation shows how the
physical entity is directed.
MAGNITUDE
less magnitude
more magnitude
DIRECTION
EQUAL MAGNITUDE;
OPPOSITE DIRECTION
SPEED VS. VELOCITY
 Velocity
has both magnitude
and direction.
 Speed has only magnitude.
You can add the
magnitudes of two
vectors together to get
the magnitude of the
resultant vector.
RESULTANT
the sum of two or more
vectors
(and takes into account
their directions)
For Example:
100 m/s +
200 m/s
300 m/s net
velocity
or resultant
velocity
Also:
100 m/s +
200 m/s
100 m/s net
velocity
or resultant
velocity
For example:
100 km/hr
10 km/hr
Net Velocity:
90 km/hr
OR
100 km/hr
WIND
10 km/hr
Net Velocity:
110 km/hr
Not all vectors occur
horizontally.
Say the wind was blowing at the
plane from the side.
WIND
The plane’s velocity is affected
by the wind.
Plane’s
velocity
Crosswind velocity
The plane’s resultant vector
would look something like this:
By using the parallelogram
method, you can represent
the resultant of two vectors.
Geometric Addition of
Vectors
Parallelograms – shapes
that have opposite sides
of equal length and are
parallel.
EXAMPLES of parallelograms
Create a parallelogram from
the two vectors --
then connect the corners.
The diagonal is the resultant
vector.
Special Case:
If you have a 90 degree
angle, you can use the
Pythagorean Theorem to
calculate the magnitude of
the resultant.
PYTHAGOREAM THEOREM
2
A
+
2
B
=
2
C
C (hypotenuse)
side A
side B
For example:
2
3
?
3
=
2
C
9 + 16 =
2
C
+
4
25 =
2
C
C = 25
C=5
2
4
SOH CAH TOA
–Sine  = opposite/hypotenuse
–Cosine  = adjacent/hypotenuse
–Tangent  = opposite/adjacent
–You can use these when you are
missing the lengths of any of the
components.
3.3 Components of Vectors
COMPONENT – one of the
vectors in a horizontal or
vertical direction whose
vector sum is equal to the
given vector.
3.3 Components of Vectors
Resolution – the
process of determining
the components of a
given vector
X
V
Y
X and Y are components (vectors)
V is the vector that is resolved
Y
V
X
Vector V has components X & Y
3.4 Projectile Motion
Projectile – any object that is
launched by some means and
continues in motion by its own
inertia
EX: a cannonball shot from a cannon
a stone thrown in the air
a ball rolling off the table
Gravity
Gravity acts DOWNWARD
A ball moving horizontally is immune
to the effects of GRAVITY on its
velocity.
There is no vertical component, only a
horizontal component.
Gravity
The instant ball is
dropped, gravity acts on it,
pulling it toward the
center of the earth.
Now it only has a
vertical component.
3.5 Upwardly-Moving
Projectiles
Figure 3.10
If a projectile had no gravity
acting on it, it would move with
this path:
Gravity changes the path of
the projectile:
Gravity pulls the projectile
towards the Earth.
Pathways of Projectiles
Objects that move at a
constant horizontal velocity
while being accelerated
vertically down, take a path
called a PARABOLA.
PARABOLA
At each point in its path the
projectile has velocity vectors such
as those below:
Each velocity vector has a vertical
and a horizontal component.
 Acceleration
is constant for a
projectile.
 Speed and velocity change at each
point along the parabolic
pathway.
 What is the speed of the projectile
at the very top of its pathway?
 What is the acceleration of the
projectile at the very top of its
pathway?
Air Resistance
Air resistance is another force that
acts on projectiles.
It changes the path of a projectile
like this:
Air Resistance
IDEAL PATH
ACTUAL PATH
Air Resistance
If air resistance is
negligible, a projectile will
rise to its maximum height
in the same amount of time
it takes it to fall back down.
Air Resistance
Without air resistance, the
deceleration of the
projectile going up is equal
to the acceleration of the
projectile coming back
down.
3.6 Fast-Moving Projectiles:
Satellites
– an object that falls
around Earth or some other
body because of its
tremendous speed, instead of
falling into it.
 Satellite
–Page 201
Chapter 3 Key Terms
 Component
 Satellite
 Projectile
 Scalar
 Resolution
 Resultant
quantity
 Vector
 Vector
quantity