Quandaries and Queries


Hello there,
here is my question:

a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex).


well, i was able to use conservation of linear momentum to derive the equation:

vf - vi = v(ex) ln ( Mi /Mf )


  • *vf is the final speed.
  • *vi is the initial speed
  • *Mi is the TOTAL initial MASS( mass of the full load + mass of the other parts )
  • and
  • *Mf is the total final mass ( mass of the full load take away the mass burnt in the first stage plus mass of the other parts )

now i really don't know how to use the above percentages to work out the masses ( in a way that all the masses inside the bracket cancel out.)

any help would be highly appreciated. thank you




Hi Hoda,

Anyway, the value would vary depending on the units you use (pounds, kilos, tons, ...) while the ratio would remain the same: After the rocket has burnt 75% of its fuel, that is, 75% * 80% = 60% of its total mass, the remaining mass is 40% of the initial mass, so that Mi/Mf should be 100/40 = 2.5


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