Advertisements for A toy balk once stated that it would rebound to a height greater than the hethe height from which it was dropped. Is this possible?

Yes, if the rebound is geared to supply more energy to it. Here is a toy that is really neat: http://www.funscienceforgirls.com/2011/04/mini-monday-momentum-from-bouncing.html

I love to do this demo. Warning: the top ball flies off at tremendous velocity.

To determine whether a toy ball can rebound to a height greater than the height from which it was dropped, we need to consider the principles of physics, specifically the conservation of energy.

When an object is dropped, it possesses potential energy due to its height above the ground. As it falls, this potential energy is converted into kinetic energy, which is the energy of motion. At the point of impact with the ground, the kinetic energy is maximized while the potential energy is minimized.

According to the law of conservation of energy, energy cannot be created or destroyed, only converted from one form to another. In the case of a bouncing ball, some of the kinetic energy is converted into potential energy during the rebound phase. However, energy is also lost as heat and sound due to the deformation of the ball and air resistance.

In real-world scenarios, no ball can rebound to a height greater than the original drop height due to energy losses and inefficiencies. The ball's rebound height will always be lower than the drop height. So, if the toy ball's advertisement claims that it can rebound higher, it is most likely an exaggeration or a misleading statement for promotional purposes.

In conclusion, it is not physically possible for a ball to rebound to a height higher than the height from which it was dropped due to energy losses and conservation principles.