#### Problem 88E

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=mgc(1ect/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 limtv. b For fixed t, use lHospitals Rule to calculate limc0+v. What can you conclude about the velocity of a falling object in a vaccum?