# Basketball and tennis ball: Part II

**Classical Mechanics**Level pending

Note: Work in the approximation where \( m_{1} \) is much larger than \(m_{2} \), which is much larger than \(m_{3} \), etc., and assume that the balls bounce elastically. If \( h = 1 \) meter, what is the minimum number of balls needed for the top one to bounce to a height of at least 1 kilometer? To reach escape velocity? Assume that the balls still bounce elastically (which is a bit absurd here). Ignore wind resistance, etc., and assume that l is negligible.