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MMLU-Pro / 10204 / Suppose that a two-stage rocket starts from rest with a mass m_1. At burn-out of…

Problem

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question

Suppose that a two-stage rocket starts from rest with a mass m_1. At burn-out of the first stage engine, the mass is m_2. If the exhaust velocity is v_0, the rocket velocity after the first stage engines quit is v = v_0ln(m_1 / m_2). Before the second stage engines are ignited, part of the mass m_2 is discarded - the mass of the first stage engines. The mass of the second stage ism_Awhen the en-gines start andm_Bwhen the engines shut down. What is the terminal velocity of the second stage?

category

physics

options

  1. v = v_0 ln [(m_1 - m_2) / (m_A * m_B)]
  2. v = v_0 In [(m_1 * m_2)(m_A*m_B)]
  3. v = v_0 ln [(m_1^2 / m_2) * (m_A / m_B)]
  4. v = v_0 ln [(m_1 * m_2) / (m_A + m_B)]
  5. v = v_0 ln [(m_1 / m_2) + (m_A/m_B)]
  6. v = v_0 In [(m_1 / m_2)(m_A+m_B)]
  7. v = v_0 ln [(m_1 + m_2) * (m_A - m_B)]
  8. v = v_0 ln [m_1 / (m_2 + m_A + m_B)]
  9. v = v_0 In [(m_1 / m_2)(m_A/m_B)]
  10. v = v_0 ln [(m_1 + m_2) / (m_A * m_B)]

src

stemez-Mechanics

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Source and history

upstream_id / Original problem ID
10204
task_id
8eab16e7-3a8f-5773-ad1c-6b8ddb49f35f
task_key
default--test--10204
task_revision_id
1
config / split
default / test

Official source

initial import