Overtime how did matter and energy in a system naturally change in physics

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.)

9.98 kg of r-134a at 300 kpa fills a rigid container whose volume is 14 l. determine the temperature and total enthalpy in the container. the container is now heated until the pressure is 600 kpa. determine the temperature and total enthalpy when the heating is completed. use data from the steam tables.

The diagram shows a boulder rolling down a hill into a valley and then up the opposite hill. at which position does the boulder have the greatest kinetic energy? a b c d