On-line Virtual Kinematics Laboratory Visualizing Interactively
Projectile Motion
Author: A. Milazzo, A. Bonanno
Dipartimento di Fisica – Università della Calabria.
Unità I.N.F.M. di Cosenza.
Introduction
Generally, the high school and university students meet many difficulties in understanding of plane
motions¹, although these are daily observed.
Such difficulties are relative either to vectorial characteristic of involved kinematic quantities and
to various ways in which the same quantities can be graphically represented. For example in the
projectile motion, vertical position (y) can be plotted as a function of horizontal position (x),
obtaining the trajectory equation (y=y(x)), but the same quantities can be also plotted versus time,
obtaining the motion laws y=y(t) and x=x(t). Other difficulties are relative to abstraction with
which normally the concept of function is usually introduced without any connection to concrete
experiences.
It is necessary to underline that, although velocity and acceleration are terms of common language,
frequently the students do not distinguish this quantities between them, with important
consequences in correct understanding of Dynamics.
Furthermore, even if mathematical instruments are relatively simple, students have serious
difficulties to derive motion equations when initial conditions are different from the standard ones
(projectile launched from origin with an initial speed).
Sometimes, some results concerning projectile motion are not easily predictable. For example, it is
not immediate to guess that a projectile in free falling and another fired from the same altitude (but
with horizontal velocity different from zero) employ the same time to hit the ground.
Currently available Multimedia² technologies can now be valuable instruments as educational³
resource in scientific matters teaching, and several web sites have been created for this purpose, like
MERLOT⁴ (Multimedia Educational Resource for Learning and on-line Teaching) proposing a
great collection of educational materials.
The Applets⁵ are the educational resources more widely used (realized in Java programming
language), because these are platform independent and allow an high degree of interaction.
About projectile motion several applets are available (or virtual laboratories) each of them focusing
peculiar features of motion.
Initial speed, shot angle, altitude from which projectile is launched can be changed , in several of
them, but rarely it is possible to insert friction air⁶.
In the setting up of this virtual laboratory we made interactive all the parameters that characterise
projectile motion, by focusing attention to the graphic representation of kinematic quantities
involved, not neglecting the recreational aspect, useful for making the use of this applet either
attractive and though-provoking.
Pedagogical aspects
Multimedia technologies are valid educational medium and present unquestioned advantages, like:
1. Greater effectiveness of the lesson
Multimedia lesson is more penetrating than the classical one, because visualization,
animations and interactivity are vehicle for immediate transmission of information, aiding
students to develop autonomous ability of elaboration in their cultural growth.
2. Improvement of learning abilities
Generally the various matters treated in Physics require imaginative ability that students
possess in diversified degrees. The presence of images and animations make possible to
overcome this limitation, making easier the scientific matters learning, and allowing the
necessary involvement to develop the collective synthesis process.
3. Possibility to realize virtual experiments
Some experiments are sometimes impossible to be realized because of limited economic
resources in scholastic institutes. Other experiments present technical difficulties to make
impossible to perform them in common scholastic laboratories. In this case it is main to
have the use of a Virtual Laboratory, useful for introducing the students to simulation of
physics phenomena and to quantitative analysis of proposed experiments.
Briefly, the concepts supported by images are immediately assimilated, supplying many
suggestions to think and consenting more time for study in depth.
A new Applet Java to implement the interactivity in the projectile motion
The applet on projectile motion, realized with purposes illustrated above, is developed as flow
diagram in figure shows:
Input
Animation
start
Setting of initial
conditions (t=0)
Calculation of
kinematic quantities:
y,x, vx,vy, ax, ay,
at the time t+∆t
Graphs
Projectile
has touched the
ground?
yes
End
no
The input data and management of animation are realized by a window, that contains (Fig.1) a cyan
panel with 3 sliders relative to initial conditions that allow to select initial velocity, shot angle, and
height from which projectile is launched. The other 3 sliders allow to change target position,
animation sleep time, and the time interval related to the number of points for projectile trajectories
painting.
Fig. 1
The window presents 6 slider for the input data, 2 checkbox and 7 button to control animation.
In the green panel are contained:
a) Four buttons, each of them allows the opening of one window.
1. “vx(t) and vy(t) graphs” (Fig.2), in which vx and vy are observed versus time.
2. “ax(t) and ay(t) graphs” (Fig.3), in which ax and ay are visualised versus time.
3. “numerical values” (Fig.4), where numerical values relative to the range and maximum height
reached are showed.
4. “motion equations” (Fig.5), in which is possible to visualise motion equations in absence and
presence of friction air.
b) Two checkbox.
Activating “slow down”, it is possible to slow down projectile motion, while selecting “friction
air”(Fig.6) the trajectory in presence of friction air can be observed, comparing it with
correspondent trajectory in absence of friction air.
Finally there are in the same window other three buttons.
1. “start”, by which the student starts the animation (Fig.7) and observes the vector speed and the
vector acceleration, with respective components.
2. “block”, that allows to stop image for few seconds, to make possible educational intervention of
teacher.
3. “clean”, that consents to clean the screen (Fig.8).
(a)
(b)
Fig.2
In these pictures the components of speed versus time in absence (a) and in presence of friction air (b) are showed.
(a)
(b)
Fig.3
The picture (a) shows acceleration at which is submitted a projectile in absence of friction air, while picture (b) shows
the components of acceleration, ax and ay
in presence of friction air.
Fig.4
The selection “numerical values” allows the visualization of numerical values for initial speed components, range and
maximum height reached from projectile, in absence and presence of friction air.
Fig.5
In the picture is showed the window containing the equations for projectile motion in the two considered cases.
Fig.6
The picture compares projectile trajectories in absence and in presence of friction air.
Fig.7
The picture highlights the reference system and decomposition of vectors with respect to it.
Fig.8
In this picture trajectories are showed for different values of motion parameters.
Conclusion
We made more guess the different concepts relative to the argument treated, recoursing to
visualization and supplying the possibility to change all the parameters involved in projectile
motion.
We have given great importance to choose of reference system, to graphic representation of
trajectories, and to laws ruling projectile motion (in absence and in presence of friction air).
All this to explain the meaning of different physics quantities, and to underline the importance of
initial conditions in the projectile motion.
Bibliography
[1] http://webphysics.davidson.edu/physletprob;
[2] A.Bonanno,”La Multimedialità come strumento per l’apprendimento modulare ed
interdisciplinare delle Scienze. Un esempio di Lezione Multimediale: Le onde elastiche” C.Costabile e R.Santarossa , “Formazione della conoscenza con le nuove tecnologie”, Convegno
Internazionale – Didattica in ambito scientifico con le nuove tecnologie – Maggio 2003
[3] Ronald L.Green, “Illuminating Physics via Web-Based self-Study” , The Physics Teachervol.39,September 2001;
[4] http://www.merlot.org/home.po;
[5] http://www.sc.ehu.es/sbweb/fisica/cinematica/bombardeo/bombardeo.htm;
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html;
[6] ] http://jersey.uoregon.edu/vlab/Cannon/index.html;
http://www.phy.ntnu.edu.tw/java/dragForce/dragForce.html;