It is possible to show, under certain assumptions, that the velocity of a falling raindrop at time is , where is the acceleration due to gravity and is the terminal velocity of the raindrop.

Suppose and .
(a) Find .
(b) How long does it take for the velocity of the raindrop to reach 99% of its terminal velocity? Round your answer to the nearest hundredth.

(a) m/s
(b) s

You can earn partial credit on this problem.