Bouncy balls put on top of each other

Bouncy balls are stacked on top of each other with decreasing mass as shown In the figure above. They are configured such that the one on the bottom is at a height of HH above the ground. The figure above shown for n=5n=5, but we can increase the number of ball to our liking.

After the balls are released, and the first ball touches the ground, each ball bounces off its neighboring ball. If vnv_{n} is the speed of the nthnth ball right after it bounces of its adjacent ball. What is the ratio of the speed of the 20th20th ball right after it bounces to the 5th5th ball right after it bounces.

Simply put what is v20v5\large{\frac { { v }_{ 20 } }{ { v }_{ 5 } }}

Details and assumptions

All the collisions that take place are elastic collisions.

Assume M1M2M3........Mn{ M }_{ 1 }\gg { M }_{ 2 }\gg { M }_{ 3 }\gg ........{ M }_{ n }.


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