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

A rocket burning it's onboard fuel while moving through space has a velocityv(t) and mass m(t) at time t. If the exhaust gasses escape with velocityv_{e}relative to the rocket , it can be deduced from Newton's Second Law of Motion that

[tex] m\frac{dv}{dt}=\frac{dm}{dt}\vec{v_{e}}

[/tex]

a. show that [tex]\vec{v}(t)=\vec{v}(0) - ln\frac{m(0)}{m(t)}\vec{v_{e}}[/tex]

b. For the rocket to accelerate in a straight line from rest to twice the speed of it's own exhaust gasses, what fraction of initial mass would the rocket have to burn as fuel?

2. Relevant equations

3. The attempt at a solution

I already solved part a, I just can't get part b.

I know that:

[tex]2\vec{v_{e}}=\vec{v}(0) - ln\frac{m(0)}{m(t)}\vec{v_{e}}[/tex]

However, I don't know where to go from here to find the initial mass the rocket would have to burn to achieve this velocity. Any ideas?

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# Vector Application Problem

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