# Projectile movement with drag

1. Oct 2, 2008

### MIKART2

Hi, i want to know what are the real effects of air (drag) in the projectile movement and free fall, i mean how drag or air resistance is calculated in both movements, with equations.

2. Oct 2, 2008

### Troels

The general differential equation for motion with airdrag is (assuming "high" velocity and fluid at rest):

$$m\frac{d \vec v}{d t}=\vec F-\gamma v^2$$

Where F is your "usual" forces, gravity etc and $$\gamma$$ is a factor that depends on the geometry of your body (shape an cross-sectional area) and the density of the fluid:

$$\gamma=\frac{\rho_{fl}A C_d}{2}$$

You can find more on this term here

The solution to this equation is that $$v\sim\tanh t$$ which converges to a constant value as t goes to infinity i. e. there is a terminal velocity.

Last edited: Oct 2, 2008