m v ˙ = m g − 1 2 ρ C D A v 2 v ( t ) = v 0 + v ∞ tanh ( g t v ∞ ) y ( t ) = y 0 + v 0 t − v ∞ 2 g ln cosh ( g t v ∞ )
C D
v 0
v ∞
y 0
Moreover, assuming the falling object to be a point mass.
Free Fall Equation (Air Drag)
modeling the fall of objects by the laws of classical mechanics, including aerodynamic drag and assuming a uniform gravitational field