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**1. Homework Statement**

I've done the first part, I'm just posting it for completeness

A rocket at rest in deep space has a body of mass m and carries an initial mass

M of fuel, which is ejected at non-relativistic speed v0 relative to the rocket. Show that

the speed of the rocket vf after all the fuel is ejected is given by

vf = v0 ln(1 + M/m)

Now consider the case of a relativistic rocket, where matter/antimatter fuel is

annihilated and expelled from the rocket as photons. Show that the final speed of this

rocket is given by

1 + M/m = [(c + vf)/(c - vf)]^0.5

**2. Homework Equations**

**3. The Attempt at a Solution**

So for the second bit: I called the mass at any instant n, and attempted to conserve momentum:

y1(n + &n)v = y2(v + &v)n - p

Where y1 is the gamme for the velocity before the emission of a small fuel element &n (the & is supposed to be a delta), and y2 is the gamme for the velocity of the rocket after emission.

y1(n - dn)v = y2(v + dv)n - E

Where E is the energy of the emitted photon(s). Here's where I get stuck. Is E = &nc^2 or E = y1 &nc^2 or something else?