# Air Resistance and projectile motion

1. May 9, 2004

### mpm166

For projectile motion, how does one take air resistance into consideration?

I have constructed a device to launch a projectile and I know how to deal with projectile motion without any air resistance, but I am unsure how I determine the range (the distance the marble/object will go) in the real world (with air resistance).

can anyone help me out?

thanks

2. May 9, 2004

### Gokul43201

Staff Emeritus
If you can do calculus, you can calculate the complete path of the object. The reason you need calculus is that the air resistance, or drag, is a continuously changing force (both in magnitude and direction), unlike gravity, which is fairly constant. The drag force usually goes like F(drag) = -cv, there v is the instantaneous velocity, and c is the drag coeeficient. The drag force always acts opposite to the direction of the instantaneous velocity, ie. always points backwards relative to the projectile. For a smooth, shiny marble, you might find that air resistance is so small that your standard result for the range wll be close enough. Try this and see how far you are off your calculated value. You could then, if necessary, tabulate the error as a function of the range (and height) for different ranges.

Another option, if you don't know calculus, but are good at programming, is the following :

Calculate the forces acting on the particle at the ends of tiny time intervals (like 1 ms). Assume the forces stay constant during the interval, and change only at the end of each interval. This way, you can construct the entire path of the projectile, given initial conditions.