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A Rocket Is Moving in Outer Space Where No External

Question 34

Multiple Choice

A rocket is moving in outer space where no external forces exist.Suppose its mass is mR and its velocity is vR at a particular time.When a mass mF of fuel is ejected,the mass of the rocket becomes (mR - mF) and its velocity increases to (vR+ A rocket is moving in outer space where no external forces exist.Suppose its mass is m<sub>R</sub> and its velocity is v<sub>R</sub> at a particular time.When a mass m<sub>F</sub> of fuel is ejected,the mass of the rocket becomes (m<sub>R</sub> - m<sub>F</sub>) and its velocity increases to (v<sub>R</sub>+ v<sub>R</sub>) .Suppose the fuel is always ejected at a constant speed v<sub>F</sub> with respect to the rocket.Derive an expression for v<sub>R</sub> as a function of m<sub>R</sub> given the rocket's initial mass and speed are m<sub>0</sub> and v<sub>0</sub>,respectively. A) v<sub>R</sub> = v<sub>0</sub> + v<sub>F</sub> ln(m<sub>R</sub>/m<sub>0</sub>) B) v<sub>R</sub> = v<sub>0</sub> - v<sub>F</sub> ln(m<sub>R</sub>/m<sub>0</sub>) C) v<sub>R</sub> = v<sub>0</sub> - v<sub>F</sub> exp(m<sub>0</sub>/m<sub>R</sub>) D) v<sub>R</sub> = v<sub>0</sub> - v<sub>F</sub> ln(m<sub>0</sub>/m<sub>R</sub> ) E) v<sub>R</sub> = v<sub>0</sub> + v<sub>F</sub> exp(m<sub>R</sub>/m<sub>0</sub>) vR) .Suppose the fuel is always ejected at a constant speed vF with respect to the rocket.Derive an expression for vR as a function of mR given the rocket's initial mass and speed are m0 and v0,respectively.


A) vR = v0 + vF ln(mR/m0)
B) vR = v0 - vF ln(mR/m0)
C) vR = v0 - vF exp(m0/mR)
D) vR = v0 - vF ln(m0/mR )
E) vR = v0 + vF exp(mR/m0)

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