Transcript Projectile Motion

Projectile Motion
Projectile Motion
What Is Projectile Motion?
•the motion of objects
moving in two
dimensions ONLY under
the influence of gravity.
Air resistance is
negligible (we can ignore
it).
•All projectiles display a
parabolic shape.
Examples of projectiles
include anything launched
or thrown into the air or space.
•The path
of a
projectile is
called its
trajectory.
•The total
distance
traveled by
a projectile
is known as
its range.
Some Vocabulary
Some Common Misconceptions….
DANGER
CLIFF
Going fast horizontally means you don’t fall as fast.
If you go fast enough, you don’t fall at all.
Gravity won’t act on you until you look down.
The Truth Is...
If gravity is the only force acting on an object,
it will accelerate at a rate of 9.8 m/s2 DOWN,
regardless of what’s happening horizontally.
In fact, if the object doesn’t have wings, jet
engines, propellers or rockets, its horizontal
motion will have absolutely no effect on its
vertical motion.
Horizontal and vertical components are
completely independent of each other.
Why? Since gravity is the only force acting on
a projectile, and it acts straight down, the
acceleration resulting is vertical. There is NO
horizontal acceleration, which means that a
projectile will maintain constant horizontal
velocity as long as it is in the air.
This is Key…
Horizontally, projectiles move with constant velocity.
….Because there’s no horizontal force to
make it go faster, or slower….Unless we
want to talk about air resistance… which
we don’t.
Vertically, projectiles move with constant acceleration.
….Because there’s a vertical force,
the earth’s gravitational pull, making
it accelerate….
Put them together and what do you get?
Horizontal Velocity Determines Horizontal
Displacement Only
Vertical Position (meters)
0
-50
0
1
2
3
4
5
-100
-150
-200
-250
-300
-350
Horizontal Position(meters)
6
7
8
The Path of a Projectile… Without Gravity
Only Equation that
you can use: v = d/t
The cannon ball moves
a constant amount with
each second.
Path of a Projectile… With Gravity
y  vi t  21 gt 2
y
The Horizontal Motion is Independent
of the Vertical Motion
Projectile Motion Summary
Horizontal
Motion
Vertical
Motion
Forces
Present
No
Yes
Gravity acting downward
Acceleration
Present
No
Yes
Gravity downward at 9.8 m/s2
Velocity
Constant
Changing
(by 9.8 m/s each second)
Projectile motion is a vector
composed of horizontal and
vertical components .
IF LAUNCHED
HORIZONTALLY
animation
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.
How Do We Solve Projectile Problems??
Consider Horizontal and Vertical
Components of Motion Independently
Vertical Equations
vyf = vyi + gt
vyf2 = vyi2 + 2g y
y = vyit + 1/2gt2
y = 1/2(vyi+vyf)t
Horizontal Equation
Vx =  x / t
Since horizontal acceleration is
zero, this is the only equation.
If an initial velocity is given, you must break it into its
horizontal and vertical components:
Vx = V cos 
Vy = V sin 
1. Draw an accurate diagram showing the
trajectory of the object.
2. Solve for the horizontal and vertical
components of the initial velocity if given.
3. Identify what you are asked to find.
(Remember you need at least 3 pieces of
vertical data to use kinematic equations .)
4. If you don’t have 3, look to the horizontal
data to find time, which is the only common
variable.