Bouncing Balls (2)

$n$ balls having masses $m_{1} >> m_{2} >> m_{3} >> ..... >>m_{n}$ , are held in a vertical stack. The bottom of the $1^{st}$ ball (lowest) is at a height $1$ meter above the ground and the bottom of the $n^{th}$ ball is at a height $40$ meters above the ground. The balls are dropped. Find the minimum number of balls required so that the top most ball ( $n^{th}$ ) reaches a height of 1 kilometer .

Details and Assumptions

• All the collisions are Elastic in nature.
• There is no variation in acceleration due to gravity with respect to height.

Inspiration - Bouncing balls and David Morin