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This Applet has several complementary applications.  First, it compares several different algorithms using simple projectile motion to determine pros and cons of each.  Second, it displays the trajectory of a projectile with or without air resistance and wind velocity.  Finally, it allows application of the knowledge of basic kinematics laws, or just plain luck, in a simple, but fun, game. 

To use:  

To go into a detailed introduction and explanation of all of the features of this applet would require a huge page.  Here, I will introduce the beginning user to the basics.  For a more in-depth explanation of the applications and theory of the applet, click on the respective links below.

The Fire button "fires" a projectile out of a cannon.

Vo, the initial velocity, can be varied, which determines the velocity with which the projectile leaves the cannon.

Theta, the initial angle, can be varied, which determines the angle at which the projectile leaves the cannon.

The effects of resistance can be modeled by clicking the Resistance check boxNotice that the path of the projectile is no longer parabolic.  

Several physical properties of the projectile can be viewed by selecting a graph from the graph choice box, currently listed as "Energy."  The available graphs are:

Energy: A graph that plots the Kinetic Energy (KE) as a function of the Potential Energy (PE).

X and Vx: A graph that plots the x position and velocity as a function of time.

Y and Vy: A graph that plots the y position and velocity as a function of time.

Error: A graph that plots the algorithmic error as a function of time, or inherently, the number of steps.

To change the view of the calculations from the Animation to the individual data points, select "Table" from the view choice bar, currently "Animation."  You can compare two different algorithms by selecting one at the top of the screen.  The available algorithms are Euler, RK2, and RK4.  You also have the choice of "Ideal," which is not a true algorithm, but rather a kinematic calculation of the ideal position of the projectile at each given point.  Note that for all reasonable purposes, RK4 will work superbly.

Finally, for the fun-spirited, select Play Game and right click on the screen to select a level of difficulty.  The object of the game is to hit the red target (without hitting the building full of innocent civilians).  

 

Those were the basics...

For a more in-depth explanation and an error analysis of the different algorithms:

Numerical Methods   

For a description of the applications of this applet for the education of projectile motion:

Projectile Motion  

For a brief description of the possibilities of the game:

Target Practice

   

 

For Java programmers interested in the program, Borland JBuilder 3.0 created the following documentation, which is a detailed analysis of all of the classes and methods in this project.

Finally, as much as I would like to claim that all of the work is a product of my own creativity and ingenuity, it is not.  Click on the following link to view the references for this project.