Can we reach escape velocity ?

On a basketball is kept another basketball of smaller size, on which a tennis ball is kept on which is a smaller ball, and so on and so forth. If the balls are released with the largest ball at height \(h\) , find minimum number of balls so that after the collision, the smallest ball reaches the escape velocity.

Note: Work in the approximation where \(m_1\) (mass of the biggest ball) is much larger than \(m_2\), which is much larger than \(m_3\), etc., and assume that the balls bounce elastically.

Assumptions and Details

  • Assume \(r_i \ll h\)
  • Radius of Earth = 6.4 X \(10^{6}\) m
  • \(h = 1\) m

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