A small block of superdense material has a mass of 3 10²⁴ kg . It is situated at a height h (much smaller than the earth's radius) from where it falls towards the earth's surface. Determine its speed when its height from the earth's surface has decreased to h/2 . The mass of the earth is 6 10²⁴ kg .

Step-by-step solution

Let the mass of the block be m = 3 10²⁴ kg and the mass of the earth be M = 6 10²⁴ kg . We have M = 2m . Since no external forces act on the earth-block system, the center of mass remains at rest. By conservation of linear momentum: M v₁ = m v₂ 2m v₁ = m v₂ v₁ = v₂ 2 where v₁ and v₂ are the speeds of the earth and the block, respectively. The height of the block from the earth's surface decreases from h to h/2 , meaning the relative distance between them decreases by h/2 . Since h is much smaller than the earth's r