On a smooth surface, a 0.140-kg toy car 1 at the velocity of 5.0 m/s collides elastically with another 0.100-kg toy car 2 with a velocity of 3.0 m/s. The
velocities of the two toy cars are in the same direction. After the collision, toy
cars 1 and 2 keep moving in the same direction with toy car 1 having a velocity of
2.8 m/s. What is the velocity of toy car 2 after the collision? Show the steps on
how you arrived at your final answer. Are the momentum and kinetic energy of
the system conserved in this collision? Explain.

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.)