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

where t is the acceleration due to gravity and is the terminal velocity of the raindrop.

(a) Find lim t→∞ v(t).

(b) Graph v(t) if v* = 1 m/s and g = 9.8m/s2. How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity?

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