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What Is The Relationship Between Distance Fallen And Time In The Air?

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Oddman answered
It is often approximated by
  d = (1/2)g*t^2 where d is the distance and g is the gravitational constant, often approximated as 32 ft/s^2 or 9.8 m/s^2. (d will be in ft or meters, accordingly) The assumption is that the object started from rest.

This is the equation for constant acceleration. Air offer resistance, so the actual distance will vary according to a different formula that will depend on shape, surface properties, and some other factors. For compact dense objects falling short distances, this is often good enough. Anything else is a fluid dynamics problem.

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