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

Suppose [math] and [math].
(a) Find [math].
(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