2.2.10 | revision #20531 | Savchenko Solutions

Statement

2.2.10. A spaceship had a velocity $$v$$ before the separation of the last stage of the launch vehicle. After discarding the last stage, its velocity became $$1.01v$$ , while the separated stage moves away relative to the ship with a velocity of $$0.04v$$ . What is the mass of the last stage if the mass of the ship is $$m_0$$ ?

Solution

Let's write the law of conservation of momentum in projection onto the axis of the ship's motion:
$$$(m_0 + m_2)v = 1.01m_0 v + (1.01 - 0.04)m_2 v$$$

From which we obtain:
$0.03m_2 = 0.01m_0 \implies m_2 = m_0 / 3$

Answer

$$m = m_0 / 3$$