I've been wrestling with this problem but to no avail. I'm hoping that someone here can give me a little nod in the right direction.
Problem statement: A thrust-beam space vehicle works bearing a sort of sail which feels the push of a strong steady laser light beam directed at it from Earth. If the sail is perfectly reflected, calculate the mass of light required to accelerate a vehicle of rest mass $m_0$ up to a fixed value of $\gamma$.
Attempt at a solution: OK. Since the sail is perfectly reflective I view as if the vehicle is emitting photons. I also realize that the momentum of the light is $p = mv = mc = m$ (since I define $c=1$). This is where I get stuck. I have been using A.P. French's Special Relativity book and read his chapter on photon emission countless of times but the solution still evades me. Any pointer will be appreciated!
edit: I should add that I've calculated the relativistic mass of the ship as $m = m_0 \gamma$ and the momentum as $p = m \gamma = m_0 \gamma ^2$