Onondaga Community College
Physics 103 & 105
EXPERIMENT ON PROJECTILE MOTION
Introduction: The motion of a projectile will be evaluated in this experiment. A projectile
is any object thrown with an initial velocity into the air usually at some angle with the
horizontal. The motion follows a curved path with a constantly changing velocity. This
complicated motion can be evaluated as two simpler motions superimposed on one
another. The motion in the ‘x’ direction is treated as one of constant velocity while that in
the ‘y’ direction is that of uniform acceleration (free fall in the absence of air friction.)
The purpose of this lab is to confirm this theory by experiment. In order to do this the
range of a projectile fired at an angle will be predicted using these ideas and compared
with the actual range. If the two compare favorably, it represents one piece of evidence
that lends support to the theory.
Y
Analysis of the Motion:
V
0
If a projectile is fired at an angle, θ0, with
an initial velocity, vo, its position in the
‘x’ direction at any time can be determined
by using the x component of the initial
velocity and time as given by: x = vox t.
θ0
X
The range of the projectile will be predicted using this equation where ‘t’ is the total time
of flight.
To determine the time of flight an analysis of the vertical motion of the object will be
made. Since the motion in the ‘y’ is that of uniform acceleration (that of free fall), the
following equation for the ‘y’ displacement applies:
y = voy t + ½ a t2
where ‘y’ is the vertical displacement from the starting position, voy is the vertical
component of the initial velocity and ‘a ‘ is the acceleration of gravity, a = -g = -9.8
m/sec2. Using this formula allows one to calculate the ‘y’ displacement for any time, ‘t’,
or knowing the vertical displacement one can determine the time at which it occurred.
The latter will be used in this experiment.
Procedure:
1.
In order to analyze the motion of the projectile at an angle, the initial velocity of
the object must first be determined. Projectile motion theory will be used to
achieve this. Fire the marble horizontally
from a measured height, ‘y1’, five times onto
V0
the carbon paper that will record the ‘x1’ distance.
Measure this distance to a weighted average of the
y1
five dots. Also, during the experiment attempt to
time the flight with the stopwatch.
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x1
Onondaga Community College
Physics 103 & 105
EXPERIMENT ON PROJECTILE MOTION
2.
From the information gathered above, calculate the initial velocity of the
projectile assuming the theory applies using the following equations:
vo  x1 ;
t1
3.
4.
y1 = ½ g t12
t1 
2y1
g
and
vo 
The firing mechanism should now be adjusted to an
angle of 30°. Once again five trials will be made with
appropriate measurements of the new ‘y2’ and ‘x2’.
The vertical displacement ‘y2’ will be used in the
calculation of the predicted range. The horizontal
measurement ‘x2’ in this part of the experiment is the
actual range of the projectile that will be used for
comparison purposes.
To calculate the predicted range the equations of
motion described in the analysis will once again be
used. The range, R = x2, will be found by:
x2 = vox t2
x1
2 y1
g
V0
θ 0 = 30°
y2
x2
where vox = vo cos θ0
The time in this relationship will be found by the use of the ‘y’ displacement as
shown below:
-y2 = voy t2 + ½ at22;
where, voy = vo sin θ0 and, a = -g = -9.8m/sec2
This will result in a quadratic equation with ‘t2’ as the variable to be determined.
Using the quadratic formula find the value of t2 and then the theoretical range of
the projectile.
5.
Compare, by finding percent difference, the experimental and predicted range of
the projectile fixed at an angle.
6.
Comment on the accuracy of the stopwatch in measuring the time of flight.
7.
Discuss the extent to which you have confirmed projectile motion theory with
attention to specific sources of error.
8.
Exercise: Calculate the time of flight for the projectile fired at an angle by
breaking the vertical motion into parts (tup + tdown = ?).
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Onondaga Community College
Physics 103 & 105
EXPERIMENT ON PROJECTILE MOTION
Write up Guide
Data – clearly presented and well organized
Title Page



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Discussion (#5 & 7)
Purpose
Method of accomplishment
Experimental set-up with
sketch
Summary of Project Motion
theory
This handout
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