Problem $3(20$ points$)$: We are designing an underwater Roomba$-$like robot to clean pools, but we're a little worried about how hard the robot will hit the bottom of the pool if somebody just tosses it into the water. The robot is spherical, has a diameter of $0\mathrm{.}15$ meters, and has a density of $1900k\frac{g}{m^3}.$ What is the terminal velocity of the robot when it is falling through pool water? Assume the water in a pool has a viscosity of $1cP$ and a density of $1000k\frac{g}{m^3},$ and that the drag coefficient at the terminal velocity is $Cd=0\mathrm{.}15.$