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Now for some examples of how these laws come into play in basketball. Take a player making a shot. Clearly, if she jumps up from the floor it is because she exerted a force on the floor --- so, by the third law, the floor exerted an equal, but opposite force, on the player, pushing her up! The player then exerts a force on the ball accelerating it out of her hands. Of course, the ball therefore acts back on the player. The result is that the ball, starting from a stop, suddenly takes off with some speed toward the basket. But the player does not take off with an equal speed the other way, because the player is *much more massive* than the ball, so by the second law, the player's acceleration will be much less! The player must be aware (through practice!) that simply accelerating the ball *directly at* the basket will not work --- the ball will end up way below the basket when it arrives. That's because gravity will cause the ball to accelerate downward throughout its flight. The player must actually aim much higher than the basket so the ball will arrive at the basket's height when it finally gets to the basket's vicinity! With that summary of a shot, you can see how each law came into play. Now you can explain any number of other events that occur in the game in a similar fashion, or through other applications of the laws.
There is one thing that occurs in both dance and basketball that aficionados recognize as special: the person who seems to be able to "hang in the air" for a long time during a jump. Unless the person has wings (or is wearing a sail, etc.), there is, of course, no way any specific individual can hang in the air longer than anyone else, unless they jump higher. The acceleration of gravity is the same for everyone, regardless of their athletic ability, or mass, or anything else. HOWEVER, some can appear to jump higher, or appear to stay higher for longer than others by using their bodies in a special way. The explanation goes as follows: The "center of mass" of your body must follow the same type of path through space during a jump as for any other person --- it is a "parabolic" path (ask your teacher about what the path looks like). The center of mass point of your body is the balance point --- if you stretched horizontally across the top edge of a roof (the peak), you'd have to position your center of mass directly over the peak to avoid tipping over to one side of the roof or the other. Now, although your center of mass has to follow a parabolic path, you can adjust the parts of your body, during the flight, to cause arms and legs, etc., to be going up, or staying at the same height, while the center of mass is falling down! The result: it looks like you're hanging in the air for a bit of time. Of course, once again, it's through practice that dancers accomplish this, not through a study of physics (but it is interesting to understand, through physics, what they are doing, and what limitations exist).
Your question (about what forces to include in your program, and how) has no good answer --- if you mean to include every force possible and every sort of particle. We don't yet know everything! Even in a practical sense it would be nearly impossible to include all we do currently know in one such program which would then yield useful information; certainly it would not be the "simplest of programs."
No scientist tries to work that way. Instead, one concentrates one's efforts on a small piece of the puzzle --- usually that's difficult enough. Nevertheless, it is possible for you to write a program to follow the motions of 1000 particles interacting in a reasonable fashion. I suggest you concentrate only on a Newtonian gravitational interaction. You will be able to accomplish this task, and probably learn a great deal in the process. Besides, after the very earliest moments of the Big Bang, gravity is the most important force in deciding the future evolution of the universe.
Each particle can be assumed to have the same mass (for simplicity!). For a particle of mass m (particle A) experiencing the gravitational force of another particle (particle B, also mass m), the force on A is toward B and of the amount Gmm/r^2 where "r^2" you might recognize to be "r squared." G is Newton's gravitational constant. Each particle A in your collection will experience a force from *each* other particle --- these individual forces add up as vectors to give the total force F acting on A.
Then, particle A therefore has an acceleration a=F/m due to the total force F acting on it Now, your program must follow the motion of each particle under the influence of the force F acting on it. This is simple in principle, but can be complicated in practice.
From reading your message it is clear you might want to get much more information than I can give you through e-mail messages. You should probably consult some introductory textbook on physics to fill in the details of what I said above. Might I suggest The Feynmann Lectures on Physics by Richard Feynman. Chapter 9 in volume 1 discuss the above calculations in basic detail. You might also benefit from looking at some similar programs. The collection of BASIC programs presented in Sky and Telescope magazine might be interesting. You can see them all by going to Sky and Telescope's website at http://www.skypub.com. Good luck.
If you assume no air resistance (or if the experiment is done in a vacuum), then the answer will not depend upon the weight of the objects in question (or any other attribute of them, such as shape).
In vacuum, if the projectile fired out of the gun is fired along a line parallel to the ground, then both projectiles will hit the ground at the same time, regardless of the velocity of the fired projectile.
Actually, there is another level of complexity that could be taken into account: both will hit the ground at the same time only if the Earth's curvature can be ignored! If the fired projective is moving fast enough (or from a high enough height) to proceed far enough toward (or past) the horizon before it hits the ground, then the fired projectile will hit the ground later than the dropped projectile. (At a truly very fast speed of firing, the projectile may never land, simply falling along a curve that never reaches the surface of the curving Earth. Then the projectile would be in orbit. That's what the Space Shuttle is doing.)
If the experiment is done in air, then the shape and weight of the projectiles would matter to some extent. For instance, a projectile of large density would fall to Earth quicker than one of the same weight but lower density (larger volume). To take an extreme example, a feather weighing the same as a penny would obviously fall slowly to Earth compared to the penny.
