Did I do this right? I'm relying on a formula the teacher gave us in class, without quite understanding it intuitively. So I'm just rewriting the formula to solve for my unknown and plugging in numbers.(adsbygoogle = window.adsbygoogle || []).push({});

A sounding rocket launched from Earth’s surface is to achieve a final speed of 1000 m/s. If the exhaust speed of the spent fuel is 2000 m/s, what fraction of the rocket’s total mass at launch must be fuel? (Assume that the engine burns rapidly enough that you may ignore any effects due to Earth’s gravity during the burn.)

[tex]

\[

v_f =v_i +v_{ex} \ln \left[ {\frac{m_i }{m_f }} \right]

\]

\[

v_f -v_i =v_{ex} \ln \left[ {\frac{m_i }{m_f }} \right]

\]

\[

\ln \left[ {\frac{m_i }{m_f }} \right]=\frac{v_f -v_i }{v_{ex} }

\]

\[

\ln \left[ {\frac{m_i }{m_f }} \right]=\frac{1000m/s-0m/s}{2000m/s}

\]

\[

\ln \left[ {\frac{m_i }{m_f }} \right]=0.5

\]

\[

\ln ^{-1}\left[ {0.5} \right]=1.6487

\]

\[

\frac{m_i }{m_f }=1.67487

\]

\[

\frac{m_f }{m_i }=\frac{1}{1.67487}

\]

\[

\frac{m_f }{m_i }=0.60653

\]

[/tex]

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# Homework Help: Rocket problem

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