The Effect of Air Resistance on a Cannon Ball

by Kjersti Raabe

Submitted : Spring 2013

This project seeks to determine the effects of air resistance on the flight of a projectile. In this scenario, we will be using a cannon ball for our calculations. We begin with the differential equations that describe the velocity of a projectile while taking into consideration the drag caused by air resistance. Using Euler's method, we solve these equations to find the components of the ball's velocity in both the x and y directions. Since position is by definition the derivative of velocity, we use Euler's method once again to find the path traveled by the cannon ball during its flight. When graphed, these calculations yield the trajectory of the cannon ball when under the influence of air resistance. Now we take the first set of differential equations, set the variable for drag equal to zero, and perform all the calculations once more. This allows us to find the trajectory of the cannon ball if there had been no air resistance. When these new results are graphed on top of the first trajectory, we can easily see the effects of air resistance on the flight of the projectile. It was found that the cannon ball would have flown approximately 600 meters higher and almost 4 kilometers farther without the presence of air resistance.

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