Chapter 4.9, Problem 79E

Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 m/s and its downward acceleration is

$a=\{\begin{array}{ll}9-0.9t\hfill & \text{if}0\le t\le 10\hfill \\ 0\hfill & \text{if}t>10\hfill \end{array}$

If the raindrop is initially 500 m above the ground, how long does it take to fall?