Alexander Fufaev
My name is Alexander FufaeV and here I write about:

Free Fall: How Bodies Fall Downwards Due to Gravity

Free fall is a motion in which a body with mass \( \class{brown}{m} \) is only subject to the influence of the gravitational force \( F_{\text g} \). No other forces, such as those due to air resistance or buoyancy, are acting. In free fall, a body experiences only the gravitational acceleration \( g \), which accelerates the body towards the ground.

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Free fall with air resistance

Without air resistance, the body would accelerate continuously until it hits the ground. The air resistance results in a constant final speed during free fall.

When the body falls, its speed increases. However, as the speed increases, the force \(F_{\text s}\), which is caused by air resistance and slows the body down, also increases:

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Formula: Flow resistance
F_{\text s} ~=~ \frac{1}{2} \, C \, \rho \, A \, v^2
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As soon as the force of air resistance and the opposing falling force \(F_{\text g} = m \, g \) add up to zero, a balance of forces is established:

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Balance of forces between gravitational force and air resistance
F_{\text g} ~=~ F_{\text S}
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Anders ausgedrückt: Es wirken keine Kräfte auf den Körper mehr, und er fällt mit einer konstanten Geschwindigkeit \(v\) zu Boden, die aus der Fallkraft \(m\,g\) sowie 4 und 4 berechnet werden kann:

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Formula: Fall speed with air resistance
v ~=~ \sqrt{ \frac{2m \, g}{C \, \rho \, A} }
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