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.

 

[astrokreng]

Hello,

Thank you for your question. The effects of air resistance, also known as drag, on projectile movement and free fall can have a significant impact on the trajectory and speed of the object.

In projectile motion, the object experiences both a horizontal and vertical component of motion. The vertical component is influenced by gravity, while the horizontal component is affected by both the initial velocity and air resistance. As the object moves through the air, it experiences a force in the opposite direction of motion due to air resistance. This force, known as drag force, can be calculated using the equation Fd = ½ρCDAv2, where ρ is the density of the air, CD is the drag coefficient, A is the cross-sectional area of the object, and v is the velocity of the object.

In free fall, the object is only influenced by the force of gravity. However, as the object accelerates towards the ground, the drag force also increases due to the increase in velocity. This can result in a decrease in the acceleration of the object, ultimately affecting its final velocity and position.

To accurately calculate the effects of drag on projectile movement and free fall, one must also take into account the shape and size of the object, as well as the density and viscosity of the air. This can be done using various equations and models, such as the drag equation mentioned above, as well as the Stokes' Law and the Reynolds number.

In conclusion, air resistance or drag can significantly impact the movement of a projectile and an object in free fall. It is important to consider these effects when studying and predicting the motion of objects in these scenarios, and to use appropriate equations and models to accurately calculate the drag force.