The equation of motion is m(dv/dt)=mg−kv, where k is a positive constant. Find v as a function of t, and find the limiting value of v as t tends to infinity; this limit is called the terminal velocity. Can you find the terminal velocity directly from the differential equation without solving it? Hint: What is dv/dt after v has reached an essentially constant value?
Consider the following specific examples of this problem.
((a)) A person drops from an airplane with a parachute. Find a reasonable value of k.
((b)) In the Millikan oil drop experiment to measure the charge of an electron, tiny electrically charged drops of oil fall through air under gravity or rise under the combination of gravity and an electric field. Measurements can be made only after they have reached terminal velocity. Find a formula for the time required for a drop starting at rest to reach 99\% of its terminal velocity.