Chapter 4.4, Problem 80E

If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is

$v=\frac{mg}{c}(1-e^{-ct/m})$

where g is the acceleration due to gravity and c is a positive constant. (In Chapter 9 we will be able to deduce this equation from the assumption that the air resistance is proportional to the speed of the object; c is the proportionality constant.)

(a) Calculate ${\lim }_{t\to \infty }v$. What is the meaning of this limit?

(b) For fixed t, use l’Hospital’s Rule to calculate ${\lim }_{c\to 0^{+}}v$. What can you conclude about the velocity of a falling object in a vacuum?