Правка разделов «Statement», «Answer»
en/2.2.10.md
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| ### Statement | |||
| − | $2.2.10.$ [Insert the problem statement] | ||
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| − | ### Solution | ||
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| − | ### Statement | ||
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| $2.2.10.$ 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: | |||
| $$0.03m_2 = 0.01m_0 \implies m_2 = m_0 / 3$$ | |||
| @@ -18,7 +12,3 @@Solution | |||
| #### Answer | |||
| $m = m_0 / 3$ | |||
| − | |||
| − | #### Answer | ||
| − | |||
| − | [Insert a concise answer or boxed result] | ||
| @@ -1,11 +1,5 @@ | |||
| ### Statement | ### 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 $m_0$? | $2.2.10.$ 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 | ### Solution | ||
| Let's write the law of conservation of momentum in projection onto the axis of the ship's motion: | Let's write the law of conservation of momentum in projection onto the axis of the ship's motion: | ||
| $$(m_0 + m_2)v = 1.01m_0 v + (1.01 - 0.04)m_2 v$$ | $$(m_0 + m_2)v = 1.01m_0 v + (1.01 - 0.04)m_2 v$$ | ||
| From which we obtain: | From which we obtain: | ||
| $$0.03m_2 = 0.01m_0 \implies m_2 = m_0 / 3$$ | $$0.03m_2 = 0.01m_0 \implies m_2 = m_0 / 3$$ | ||
| @@ -18,7 +12,3 @@Solution | |||
| #### Answer | #### Answer | ||
| $m = m_0 / 3$ | $m = m_0 / 3$ | ||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||