Exercise $2\mathrm{.}1\mathrm{.}9$ A $5$ kilogram rock is dropped from a bridge that is $200$ meters above the surface of a river that is $10$ meters deep. As the rock falls through the air, the force of resistance on the rock $($in newtons$)$ is equal to $0\mathrm{.}8$ times the velocity in meters per second $($the units on $0\mathrm{.}8$ are newtons per meter per second$).$ As the rock falls through the water the resistance in newtons is equal to $5\mathrm{.}0$ times the rock's velocity $($same units as the $0\mathrm{.}8$ coefficient$).$ Acceleration due to gravity is $9\mathrm{.}8$ meters per second squared.

$($a$)$ How long after the rock is released will it hit the water?

$($b$)$ How long after the rock hits the water will it hit the bottom of the river?

$($c$)$ What is the rock's velocity when it hits the bottom?