A rocket of initial rest mass \(M_{0}\) has a propulsion system that accelerates it by converting matter into light with negligible heat loss and directs the light in a collimated beam behind it. The propulsion system is turned on for some period of time during which the speed of the rocket is boosted by speed \(v\). Use energy and momentum conservation to show that the final rest mass of the rocket is given by \(M_{v}=M_{0} \sqrt{(c-v) /(c+v)}\).