page_title: Free fall
section_title: Uniform gravitational field with air resistance
hierarchical_section_title: Free fall / Free fall in Newtonian mechanics / Uniform gravitational field with air resistance
caption_attribution_description: English: This diagram shows the acceleration of an idealized (spherical) meteoroid when entering the Earth's atmosphere at different initial velocities. As the density of the atmosphere increases in accord with the barometric formula, the meteoroid experiences more and more Newton drag. The initial velocities are 35, 25 and 15 km/s, where a higher peak corresponds to a higher initial velocity. An acceleration of 1 km/s² is about 100 g. The meteoroid considered here consists of iron. It has a volume of 1 cm³ and a mass of about 7.874 gramms.
context_page_description: In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
  An object in the technical sense of the term "free fall" may not necessarily be falling down in the usual sense of the term. An object moving upwards would not normally be considered to be falling, but if it is subject to the force of gravity only, it is said to be in free fall. The moon is thus in free fall.
  In a roughly uniform gravitational field, in the absence of any other forces, gravitation acts on each part of the body roughly equally, which results in the sensation of weightlessness, a condition that also occurs when the gravitational field is weak.
  The term "free fall" is often used more loosely than in the strict sense defined above. Thus, falling through an atmosphere without a deployed parachute, or lifting device, is also often referred to as free fall.
context_section_description: This case, which applies to skydivers, parachutists or any body of mass, , and cross-sectional area, , with Reynolds number well above the critical Reynolds number, so that the air resistance is proportional to the square of the fall velocity, , has an equation of motion
  where  is the air density and  is the drag coefficient, assumed to be constant although in general it will depend on the Reynolds number.
  Assuming an object falling from rest and no change in air density with altitude, the solution is:
  where the terminal speed is given by
  The object's speed versus time can be integrated over time to find the vertical position as a function of time:
  Using the figure of 56 m/s for the terminal velocity of a human, one finds that after 10 seconds he will have fallen 348 metres and attained 94% of terminal velocity, and after 12 seconds he will have fallen 455 metres and will have attained 97% of terminal velocity. However, when the air density cannot be assumed to be constant, such as for objects falling from high altitude, the equation of motion becomes much more difficult to solve analytically and a numerical simulation of the motion is usually necessary. The figure shows the forces acting on meteoroids falling through the Earth's upper atmosphere. HALO jumps, including Joe Kittinger's and Felix Baumgartner's record jumps, also belong in this category.
caption: Acceleration of a small meteoroid when entering the Earth's atmosphere at different initial velocities.
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