Laboratory 4
Projectile Motion
Introduction
We have spent the past two laboratories investigating onedimensional motion. In Laboratory 2,
we looked at a situation where an object was subject to a constant force (and, hence, acceleration)
while in Laboratory 3 we looked at a situation where the force was not constant. However, in both
of these labs, the motion of the objects and the net forces they experienced were
parallel
; the forces
served to speed the objects up or slow them down, but the objects always moved along the same
[onedimensional] line.
In most of life, things are not this simple.
In projectile motion, which we will explore today,
things get more complicated, because the acceleration can be perpendicular to the object’s velocity,
parallel to it, or somewhere in between depending on how the object is launched. This laboratory
marks the start of our exploration of twodimensional motion. In twodimensional motion, the
net force and velocity vectors lie in a plane, but are not necessarily parallel to each other. This
describes the majority of situations you will encounter in the rest of the course.
Theoretical Section: TwoDimensional Motion
In Table 1 of Laboratory 2, we encountered four equations relating the variables
x
(displacement),
v
0
(initial velocity),
v
(final velocity),
a
(acceleration), and
t
(time). Recall that each equation
allows you to use three variables to solve for a fourth; the fifth is ignored. To extend these equations
to twodimensional motion, we must simply apply the principle of
dimensional independence
,
which means that forces, displacements, accelerations, etc.
happening in one direction do not
affect those happening in a perpendicular direction. Because of this very important principle, we
can write two sets of equations, using subscripts to denote velocities and accelerations happening
in the
x
and
y
directions, shown in Table 1. The only variable that is the same for both dimensions
is time; we will exploit this fact repeatedly in our analyses of twodimensional motion.
One cannot study twodimensional motion effectively without understanding the ideas of
vector
addition
and
component vectors
, which we already encountered in Laboratory 2. A full analysis
of these concepts can be found in any introductory physics text.
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Parameter
x
dimension
y
dimension
Initial position
x
0
y
0
Position
x
y
Initial velocity
v
0
x
v
0
y
Final velocity
v
x
v
y
Acceleration
a
x
a
y
Time
t
t
Table 1:
All of the variables for the
x
and
y
dimensions are distinct, except for time.
Theoretical Section: Projectile Motion
A
projectile
is any object propelled through space by a force that ceases after it is launched.
While it is in flight, the only force that acts on it is gravity. Using the coordinate system shown in
Figure 1, we can make a table showing the relevant kinematic quantities in the
x
and
y
directions
(see Table 1).
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 Spring '11
 Gerson
 Acceleration, Velocity, video capture, twodimensional motion, air table

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