To illustrate the use of a multistage rocket consider the following: (a) A certain rocket carries 60% of its initial mass as fuel. (That is, the mass of fuel is
0.6mo)
What is the rocket's final speed, accelerating from rest in free space, if it burns all its fuel in a single stage? Express your answer as a multiple of
vex.
(b) Suppose instead it burns the fuel in two stages as follows: In the first stage it burns a mass
0.3mo
of fuel. It then jettisons the first-stage fuel tank, which has a mass of
0.1mo
, and then burns the remaining
0.3mo
of fuel. Find the final speed in this case, assuming the same value of
vex
throughout and compare.