(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rocket of initial mas M, of which M-m is fuel, burns its fuel at a constant rate in time tau and ejects the exhausts gases with constant speed u. The rocket starts from rest and moves vertically under uniform gravity . Show that the maximum speed achieved by the rocket is u ln([tex]\gamma[/tex])-g[tex]\tau[/tex] and that its height at burnout is

u[tex]\tau[/tex](1-ln([tex]\gamma[/tex])/([tex]\gamma[/tex]-1) where [tex]\gamma[/tex]=M/m[assume that the thrust is such that the rocket takes off immediately.)

2. Relevant equations

3. The attempt at a solution

I had no trouble finding v, I had trouble integrating v to obtain the height. v=u ln (gamma)-g*tau . h=[tex]\int[/tex]v dt= [tex]\int[/tex]u*ln(m_{0}/m(t))-.5*gt^2

u is treated as a constant I think since I am integrating v with respect to dt. [tex]\int[/tex]ln([tex]\gamma[/tex])=[tex]\gamma[/tex]*ln([tex]\gamma[/tex])-[tex]\gamma[/tex]. Now I am stuck on this part of the solution.

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# Homework Help: Rocket motion problem

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