Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. The
astronaut has her lucky penny in her hand behind her
back as the space pirates break into the control room.
She has just locked the controls so that the ship is
accelerating in the direction of the control room's ceiling.
Simon wants the astronaut to use the penny to hit a
button on the control panel to turn off the lights and
escape. The button is located a short distance behind
and below the astronaut's hands.

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)