Asmall metal ball is suspended from the ceiling by a thread of negligible mass. the ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone. the acceleration of gravity is 9.8 m/s 2 . r v g ℓ m θ what is the speed of the ball when it is in circular motion? answer in terms of g, ℓ and θ.

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.)