Predicting the Range of a Projectile by the Construction of Experimental Models that recognize Air Resistance

A system was developed in the laboratory to study the range of several projectiles in the presence of a uniform gravitational field. Air resistance was recognized in this experiment. We identified the drag coefficient of each projectile by studying the corresponding terminal velocities. Assuming that the frictional force on each projectile was proportional to V or V-2, we derived two models that describe the range of the projectiles. The linear model was patterned after a method found in Atam Arya\u27s Introduction to Classical Mechanics. The quadratic model contained inseparable variables and was therefore solved using the computer package Mathematica. We then tested these unique models against the ** traditional model which disregards the presence of friction. For our particular system, we found that our experimental models were more accurate than the general equation for determining the range of a projectile. **Traditional- That is, the classic equation R = (vo-2*Sin(2Theta))/9.8