Projectile Motion
Motion In Two Dimensions
We restrict ourselves to objects thrown near the Earth’s surface so that gravity
can be considered constant.
Objectives
1. For a projectile, describe the changes in the
horizontal and vertical components of its velocity,
when air resistance is negligible.
2. Explain why a projectile moves equal distances
horizontally in equal time intervals when air
resistance is negligible.
3. Describe satellites as fast moving projectiles.
Projectile motion applies to sports.
Projectile motion applies to destructive
projectiles.
Other
Examples
Of
Projectiles
A projectile is any object that moves through
the air or through space, acted on only by
gravity (and air resistance).
The motion of a projectile is determined only
by the object’s initial velocity, launch angle and
gravity.
1, 2
Projectile motion is a combination of horizontal
motion and vertical motion.
The horizontal motion of a projectile is constant
because no gravitational force acts horizontally
3, 4
The vertical motion of a projected object is
independent of its horizontal motion.
5
Let's say a Wiley coyote runs off a cliff. As he
leaves the cliff he has a horizontal velocity.
As soon as the coyote leaves the cliff he will
experience a vertical force due to gravity.
This force will cause him to start to accelerate
in the vertical direction.
As he falls he will be going faster and faster in
the vertical direction
The horizontal and
vertical components of
the motion of an object
going off a cliff are
separate from each other,
and can not affect each
other.
Y
X
In a lot of books you will see the horizontal component
called x and the vertical component called y.
The x-component of a projectile’s
motion is there from the start, and
stays the same the entire time.
The y-component
of a projectile’s
motion doesn’t
even exist at the
beginning, but
grows bigger as
the object falls.
6
The vertical motion of a projectile is nothing more than
free fall with a constant acceleration due to gravity.
7
A projectile, once projected, continues in
motion by its own inertia and is influenced
only by the downward force of gravity.
8
A projectile moves horizontally with constant
velocity while being accelerated vertically. The
result is a motion in a curved path.
9
Gravity accelerates objects
downwards, but is unable to
affect the horizontal motion of a
projectile.
10
The path of a projectile is called its trajectory.
The trajectory of a projectile in free fall is a parabola.
The total
distance
traveled by a
projectile is
known as its
range.
11, 12, 13
Horizontal Shot.
If the barrel of a rifle is horizontal to the surface of
the earth when fired, the bullet never rises above
the barrel, and gravity causes an immediate
descent.
Projectile Vectors
Horizontal and vertical components are represented as
vectors.
14
An object projected
horizontally will
reach the ground in
the same time as
an object dropped
vertically.
No matter how
large the horizontal
velocity is, the
downward pull of
gravity is always
the same.
15, 16
The cannonball falls the same amount of distance as it did
when it was merely dropped from rest
Projectile Motion Summary
Horizontal
Motion
Forces
Present
No
Acceleration
Present
No
Velocity
Constant
Vertical
Motion
Yes
Gravity acting downward
Yes
Gravity downward at 9.8
m/s2
Changing
(by 9.8 m/s each second)
Horizontally launched projectile
Horizontal velocity is constant. Vertical velocity is changing
due to gravitational acceleration..
Vertically launched projectile
The horizontal velocity component remains the same size
throughout the entire motion of the cannonball.
If projectiles are launched at the same speed, but at different
angles, the height and range is of the projectile are affected.
17
Sports Trivia
Maximum range is achieved if the projectile is
fired at an angle of 45 degrees with respect to
the horizontal.
18
0°, 90°minimum range
45°maximum range
Angle with Longest time in
Air? 90°
Which angle of projection causes a projectile
to stay in the air longer? 50 or 70 degrees
70 degrees,
(closest to 90,
longer time in air)
http://library.thinkquest.org/27585/lab/sim_pirates.html
http://library.thinkquest.org/2779/Balloon.html
If it takes 4 seconds for a projectile to rise to its peak, then
it takes 8 seconds to move through the air from start to
finish. Why?
19
Because the vertical
velocity changes by
9.8 m/s (in the upward or
downward direction) each
second.
For example
If a projectile is moving
upwards with a velocity
of 40 m/s at 0 seconds,
then its velocity will be:
30 m/s after 1 second
20 m/s after 2 seconds,
10 m/s after 3 seconds,
40 m/s after 8 seconds.
20, 21
Free Fall Results
•
•
•
•
Horizontal motion is constant
Vertical Motion is accelerated
Rise time = Fall Time
Final speed = Initial speed
When the effect of air resistance is significant,
the range of a projectile is diminished and the
path is not a true parabola.
22
In the case of air resistance, the path of a high-speed
projectile falls below the idealized path and follows
the solid curve.
Computer-generated trajectories of a baseball with and without drag.
23
In Conclusion
A projectile is any object upon which the only force
is gravity.
Projectiles travel with a parabolic trajectory due to
the influence of gravity.
There are no horizontal forces acting upon projectiles
and thus no horizontal acceleration.
The horizontal velocity of a projectile is constant.
there is a vertical acceleration caused by gravity
(9.8 m/s).
The horizontal motion of a projectile is independent
of its vertical motion.
Test your knowledge
Suppose a snowmobile is equipped with a
flare launcher which is capable of launching
a sphere vertically. If the snowmobile is in
motion and launches the flare and maintains a
constant horizontal velocity after the launch,
then where will the flare land (neglect air
resistance)?
Test your knowledge
Suppose an airplane drops a flare while it
is moving at constant horizontal speed at
an elevated height. Assuming that air
resistance is negligible, where will the flare
land relative to the plane?
A. Directly below the plane.
B. Below the plane and ahead of it.
C. Below plane and behind it.
Why does the horizontal component of a
projectile’s motion remain constant?
Because no force acts on it horizontally.
Why does the vertical component of a
projectile’s motion undergo change?
Because gravity is pulling it downward.
How does the vertical distance a projectile
falls below an otherwise straight-line path
compare with the vertical distance it would
fall from rest in the same time?
The vertical and horizontal distances are
equal.
A projectile is launched vertically at 100
m/s. If air resistance can be neglected, at
what speed does it return to its initial
level?
100 m/s
A rock is thrown upward at an angle.
What happens to the horizontal
component of its velocity as it rises?
(Neglect air resistance.)
(a) it decreases
(b) it increases
(c) it remains the same
In baseball which path would a home
run most closely approximate?
(Neglect air resistance.)
(a) hyperbolic
(b) parabolic
(c) ellipse
A horizontally traveling car drives off of a
cliff next to the ocean. At the same time
that the car leaves the cliff a bystander
drops his camera. Which hits the ocean
first? (Neglect air resistance.)
(a) car
(b) camera
(c) they both hit at the same time
When a rifle is being aimed at a distant
target, the barrel should be lined up so that
it points:

A. Slightly higher than the target
B. Exactly at the target
C. Slightly lower than the target