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 $=$

$90\mathrm{.}9$t$$ if$0$ t $100$ if$$ t $>10.$

Find the velocity v $($in m$/$s$)$ of the raindrop for time

$0$ t $10.$

v$($t$)=$

$9$t$0\mathrm{.}45$t$2+10$

m$/$s

If the raindrop is initially $700$ m above the ground, find the height s of the raindrop $($in meters$)$ after it falls for $10$ seconds.

s$(10)=$ m

How long $($in seconds$)$ does it take to fall? $($Round your answer to two decimal places.$)$

s