A blue puck with mass 0.0400 kg, sliding with a speed of 0.200 m/s on a frictionless, horizontal surface, makes a perfectly elastic head‐on collision with a red puck with mass m, initially at rest. After the collision, the velocity of the blue puck is 0.0500 m/s in the same direction as its initial velocity. (a) Find the mass m of the red puck, and (b)the velocity (magnitude and direction) of the red puck after the collision

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.)