Phys-211 Project Projectile Motion James Gentry III Daniel Arnold

## Introduction

 Physics define the rules by which we live our physical existence. Many of us go about our day to day lives without any true understanding of the Laws which govern how we interact with our surroundings. Physics is our way of making sense of the forces which act upon us and shape the way we accomplish even the most menial of tasks. From walking to driving to playing a game of catch; Anyone can see physics in action. A computer game programmer must take a special look at the forces at work around us. The programmers who code flight simulators, first person shooters, and similar games, often need to model their virtual world as closely as possible to our own. In this project we will look at the first person combat simulator called "Tribes™", by Dynamix. We will focus mainly on projectile motion, but we will also discuss the challenges the programmers had in computing ranges for projectiles, friction, and momentum. Also touched on, will be how they succeeded and failed in their efforts.

## Challenges

 In Tribes™, the programmers had to create an environment for the players. The challenge is to model our real life Laws of physics as accurately as possible. However, programmers are not physicists and it would take a super computer to accurately model all physics in a real world environment. This environment includes a variable gravity. This was important to game play in that the programmers could now make different worlds for the players to fight in. A planet of different mass will obviously have a different gravity. The following equation shows the horizontal range of a projectile, R = (V²o / g) * sin(2Ø) (Halliday, et al 60-64). Where R is the range, Vo is the initial velocity, g is gravity, and Ø is the angle the projectile is fired at. It is easy to see from the equation that a change in gravity will affect the total horizontal range achievable by a projectile. An interesting note is that a 45 degree angle will provide the maximum horizontal range for the projectile, no matter what the force of gravity is. (Assuming gravity does not equal zero). We are neglecting air resistance in our calculations, as did the makers of Tribes™. When the programmers did this however, they got some unexpected, yet fun results. While projectile motion was not affected greatly, a person flying in the game could reach insane speeds, as there was no terminal velocity. This was possible because a player could hit the 'jump' button very fast and 'ski' down a slope. When skiing down a slope, the player object was not affected by any frictional force from the ground. Combined with no air resistance, it was possible to project your player at unheard of velocities. This was obviously a huge oversight on the part of the programmers, however, it did make the game a lot more fun!

## History of Projectile Motion

 Galileo was the first person who ever accurately described projectile motion. He was the one who first broke down motion into it's separate horizontal and vertical components (Web 1). Galileo even took this idea further with his realization that there was more than one force at work upon the projectile. Utilizing these revolutionary insights, he then concluded that the curve of ANY projectile is a parabola. It was this idea that let us examine how two objects in a vacuum, even if of different shape and mass, will hit the ground at the exact same time, if both are dropped from the same height. It does not take much imagination to see how the concept of projectile motion could be used in a military setting (Lab 25). From firing a cannon ball, to dropping a bomb out of an airplane, to firing a Volkswagon sized bullet out of a huge battleship gun, the equations of projectile motion allow us to accurately hit a target from great distances (Web 2).