# 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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