In Chapter 9 we will be able to show, under certain assumptions, that the velocity v(t) of

Question:

In Chapter 9 we will be able to show, under certain assumptions, that the velocity v(t) of a falling raindrop at time t is
V(t) = v* (1 - e-gt/v*)
where t is the acceleration due to gravity and v* is the terminal velocity of the raindrop.
(a) Find limt→∞ v(t).
(b) Graph v(t) if v* = 1 m/s and g = 9.8 m/s2. How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity?