One popular, if dangerous, classroom demonstration involves holding a baseball an inch or so directly above a basketball that you are holding a few feet above a hard floor, and dropping the two balls simultaneously. The two balls will collide just after the basketball bounces from the floor; the baseball will then rocket off into the ceiling tiles, while the basketball will stop in midair. 

(a) Assuming that the collision of the basketball with the floor is elastic, what is the relation between the velocities of the balls just before they collide? 

(b) Assuming the collision between the two balls is elastic, use the result of Part (a) and the conservation of momentum and the conservation of energy to show that, if the basketball is three times as heavy as the baseball, the final velocity of the basketball will be zero. (This is approximately the true mass ratio, which is why the demonstration is so dramatic.) 

(c) If the speed of the baseball is v just before the collision, what is its speed just after the collision?