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Valter edited Sep 3, 2026, 6:50 PM

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		+	### Statement
		+
		+	$2.2.10.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	### 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
		+	$m = m_0 / 3$
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$2.2.10.$ [Insert the problem statement]

			### Solution

			### 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
			$m = m_0 / 3$

			#### Answer

			[Insert a concise answer or boxed result]