Textbook Problem

Velocity in a Resisting Medium The velocity v of an object falling through a resisting medium such as air or water is given by

$v=\frac{32}{k}\left(1-e^{-kt}+\frac{v_{0}k{e}^{-kt}}{32}\right)$

where v₀ is the initial velocity, t is the time in seconds, and k is the resistance constant of the medium. Use L'Hôpital’s Rule to find the formula for the velocity of a falling body in a vacuum by fixing v₀ and t and letting k approach zero. (Assume that the downward direction is positive.)