How Does Air Resistance Affect Projectile Motion and Free Fall?

[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.

 

[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 http://en.wikipedia.org/wiki/Drag_equation"

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.