Freefall From Specified Height

For a sphere of radius r = cm

and density ρ = kg/m³ = gm/cm³

the mass is m = gm.

Assume the object has a drag coefficient C = (the default value is C = 0.5 for a sphere)

and is falling through air with density ρ* = kg/m³ (the default value is 1.29 kg/m³).

Under these conditions, it's terminal velocity will be
v_t = m/s = km/hr = mi/hr

and its characteristic time is
τ = s.

If dropped from rest at height h = m = ft

it will reach the ground at velocity
v_impact = m/s = ft/s = km/hr = mi/hr

at time t_impact = s.

For comparison, if there were no air friction the object would impact with velocity v = m/s at time t = s.

If dropped from great height so that it spends most of the time at terminal velocity, the time of fall would approach h/v_t = s. This number represents a lower bound for the fall time since it assumes that the object falls at the terminal velocity for the whole time and there is always a finite time required to reach the terminal velocity. For heights large enough that the acceleration time is very small compared to the total time, the calculated fall time should approach this limit from above.