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Horizontally Launched Projectiles
A ball rolling off the table is an excellent example of an object
thrown into the air with horizontal initial velocity (velocity at
the time when the object is launched). The ball becomes
airborne when leaving the table.
If the ball rolls along the table with constant horizontal velocity,
then the moment it leaves the table, it has the same horizontal
velocity with which it rolled along the table and zero vertical
velocity.
The ball would continue its motion with the same speed and
direction unless there is an acceleration.
In the horizontal direction, there are no forces on the motion which
means that nothing can give the object horizontal acceleration.
Horizontal velocity remains CONSTANT, because we neglect air
resistance in our calculations, and the ball covers equal distances in
equal intervals of time.
In vertical direction there is gravitational acceleration.
The projectile accelerates downward.
When these two motions are combined - vertical free fall motion and uniform
horizontal motion - the trajectory will be a parabola.
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Projectiles Launched at an Angle
Often, the projectiles are launched at an angle. To solve
the problem, we resolve this initial velocity into its
vy
horizontal and vertical components.
Horizontal component vx is constant
throughout the motion.
v
q
vx
Vertical component vy is decreasing on the way
up, becoming zero at the top, and increasing on
the way down.
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Horizontal component of motion for a projectile is
completely independent of the vertical component of
the motion. Their combined effects produce the variety
of curved paths - parabolas that projectile follow.
Zookeeper who found the special way to feed monkey banana.
The
zookeeper
aims atacting
the monkey
If there
was no gravity
on
and
shoots
the banana
fast .
either
the banana
or thevery
monkey,
The
The
zookeeper
banana
reaches
aims
above
the monkey
the
banana
moves
in a straight
line and
monkey’s
before
monkey
has
banana
misses
very
the monkey
does not
fallfallen
once
he the
monkey,
far.
over
lets go ofmoving
the tree.
As his
such,
a banana
passes
far above
theatmonkey's
bananaas
aimed
directly
the monkey
as
was
willit hit
theoriginally
monkey.aimed.
The zookeeper aims at the monkey
and shoots the banana with a slow
speed . Banana hits the monkey after
the monkey has fallen considerably far.
In conclusion, the key to the zookeeper's
dilemma is to aim directly at the monkey.
Both banana and monkey experience the
same acceleration since gravity causes all
objects to accelerate at the same rate
regardless of their mass.
Since both banana and monkey experience
the same acceleration each will fall equal
amounts.
When an object is launched at an angle, it has an initial velocity
that can be resolved into horizontal and vertical components.
The horizontal component of
initial velocity IS CONSTANT
(i.e. has no acceleration) because
there are no forces acting upon it.
The vertical component of initial
velocity changes because it
experiences downward
acceleration due to the force of
gravity.
Remind your self continuously: forces are not required for an object to be
moving; once in motion, the presence of forces will only serve to accelerate
such objects.
Check Your Understanding -- The Truck and The Ball
Imagine a pickup truck moving with a constant speed along a city street. In
the course of its motion, a ball is projected straight upwards by a launcher
located in the bed of the truck. Imagine as well that the ball does not
encounter a significant amount of air resistance.
Where will the ball land?
1) In front of the truck, 2) In the truck, 3) Behind the truck,
4) We need to know the velocity of th e truck and ball to answer
How do you
know?
Range of Projectile Motion (when
starting and ending height are
equal)
750
600
450
300
R = 2 vi2 sinθ cos θ
the same range is obtained for two
projection angles that add up to 900
Projectile thrown with the same
speed at 300 and 600 will have
the same range. The one at 300
remains in the air for a shorter
time.
This is our only new
equation!
150
What if we have air resistance?
IDEAL
PATH
ACTUAL
PATH
Air resistance shortens the range of
the object, and the path is no longer a
parabola. You won’t need to
mathematically solve this, but you DO
need to be able to describe how air
resistance affects the motion.

If a projectile launches and lands at the same
height, what affects how far it travels?
Initial speed and angle

What affects how long a projectile stays in the
air?
Height of launch relative to landing, and the
vertical component of initial velocity.



How does a projectile’s vertical velocity change
over time?
It becomes more negative.
How does a projectile’s horizontal velocity
change over time?
It doesn’t change (if air resistance is ignored)
How does a projectile’s acceleration change over
time?
It doesn’t change (always 9.81 m/s2 down)
Closure
Exit Ticket
Homework
To solve projectile motion problems, you must
separate the horizontal and vertical components
of motion.
1)
2)
3)
4)
Resolve the launch velocity to find the vix and viy. (Use
SOH CAH TOA)
Divide your paper into two sections – one for
horizontal and one for vertical
Write the relevant equations and known variables in
the appropriate sections
Recognize that horizontal and vertical sides are linked
by time in the air. You may use time to find other
variables on either section.