Projectile Motion
Projectile Motion
Today’s Objectives:
Recognize examples of projectile motion,
Recognize that the horizontal and vertical
components of a projectile’s motion are
independent of each other, and
Resolve vectors into their components,
and apply the kinematic equations to
solve problems involving projectiles.
What Is Projectile Motion?
Projectile Motion is the motion of
objects moving in two dimensions
under the influence of gravity. Air
resistance is negligible (we can ignore
it).
EXAMPLES OF PROJECTILES
Examples of projectiles include anything
launched or thrown into the air such as
cannon balls, baseballs, pumpkins,
soccer balls, tennis balls, handballs,
racquetballs, people, four-square balls,
softballs, mothballs, fireworks, water from
rain clouds or from a hose…
There Are Some Common
Misconceptions….
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.
They are completely independent of
each other.
This is Key…
…To understanding projectiles:
Horizontally, projectiles move with
constant velocity.
Vertically, projectiles move with
constant acceleration.
WHY? Lets Consider a Little Information
About… Newton’s Laws of Motion
Newton’s First Law of Motion, also known as the
Law of Inertia, states that a body in motion will
remain in motion at constant velocity, unless acted
upon by an unbalanced force (and that a body at
rest will remain at rest).
Therefore, if there were no gravity, an object fired
from a cannon off a hilltop would continue along a
straight-line path at constant velocity forever and
ever…the horizontal motion remains constant.
The Path of a Projectile… Without Gravity
The cannon ball moves
a constant amount with
each second.
Path of a Projectile… With Gravity
y  vi t  21 gt 2
y
WATCH THE NUMBERS
The Horizontal Motion is
Independent of the Vertical Motion
HORIZONTAL VELOCITY is STILL Constant
WHAT DOES THE PILOT SEE (LOOKING DOWN)
IF THE PLANE WERE MADE OF GLASS ?
What’s a Satellite??
How Do We Solve Projectile Problems??
Consider Horizontal and Vertical
Components of Motion Independently
Vertical Components:
y - vertical displacement
g - vertical acceleration (9.8 m/s2)
vyi - initial vertical velocity
vyf - final vertical velocity
t - time
Horizontal Components:
 x - horizontal displacement
vxi = vxf - horizontal velocity
t - time
How Do We Solve Projectile Problems??
Vertical Equations
vf = vi + at
vf2 = vi2 + 2a y
y = vit + 1/2at2
y = 1/2(vi+vf)t
y = vft - 1/2at2
These equations assume that
down is negative!!
vyf = vyi - gt
vyf2 = vyi2 - 2g y
y = vyit – 1/2gt2
y = 1/2(vyi+vyf)t
y = vit + 1/2gt2
Horizontal Equation
x = vxt Since horizontal acceleration is
zero, this is the only equation.
How Do We Solve Projectile
Problems??
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. Complete a data table using given and implied
data, based on an appropriate sign convention
(you assign).
4. Identify what you are looking for. Remember
you need at least 3 pieces of vertical data to use
kinematic equations… if you don’t have 3, look
to the horizontal data to find time, which is the
only common variable.
‘Human’ Cannonball
Mr. Maroo is launched from a cannon with
an initial velocity of 18 m/s at an angle of 25°
with the horizontal. (a) How high will he go?
(b) Where should a safety net be placed so
that he lands safely? (c) How much time
does he spend in the air?
Given:
25°
Vi=18 m/s
Vyi=18 m/s sin 25°= 7.6 m/s
Vxi=18 m/s cos 25°= 16.3 m/s
V H
Vyi=7.6 m/s Vxi=16.3 m/s
g=-9.8 m/s2
Vyf= 0 m/s
Practice With an Applet
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html