If an object of mass is dropped from rest, one model for its speed after seconds, taking air resistance into account is:
Where is the acceleration due to gravity and 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.
(a) Calculate . Your answer may depend on , , and .
(b) For fixed , use L'Hospital's rule to calculate . Your answer may depend on , , and .
You can earn partial credit on this problem.