Two billiard balls of equal mass move at right angles and meet at the origin of a xy coordinate system. One is moving upward along the y axis at 2.1 m/s and the other is moving to the right along the x-axis with a speed of 3.8 m/s. After the elastic collision, the second ball is moving along the positive y-axis. What is the final direction of the first ball, and what are their two speeds?

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.)