Math physics question Need help, PLEASE! THANKS!?

Question

If you had a large ball and a small one and held the small ball over the big one touching it, dropped the balls together from chest height so that the smaller ball rides the big ball during the fall, how would the big ball move after they collided and would it be different from it's motion if it was dropped from the same height without the smaller ball? How would the smaller ball move after it collided with the larger one and would it's motion be different if dropped from the same height without the large ball? Why?

Answer 1

With the small ball riding the large one down an interesting thing happens upon impact.  Assuming high density, the small ball will bounce off the large ball as the large one bounces off the ground. If there is any space between the balls a portion of the kinetic energy transferred to the larger ball from hitting the ground will be transferred to the smaller ball.  the smaller ball will rise higher than expected and the larger ball will rise less than expected.  This will occur to an extent even if they are touching but less dense.  The amount of deformation each undergoes plays a part.  

If balls are dropped without interfering with each other,  each will rebound as expected.  While touching they will share net kinetic energy.  This is what will make the smaller ball go higher and larger ball go less high.