Compare the performance of a one-stage rocket with that of a two-stage rocket having similar fuel mass and structure mass. Rocket \(A\) has mass \(M_{A}=11 \mathrm{t}\), of which \(m_{A}^{c}=9.7 \mathrm{t}\) is the fuel mass, and its engines are capable of emitting exhaust gases with velocity \(v_{g}\). The \(B\) rocket, with the same total mass as the first one, consists of two stages with \(M_{B 1}=10 \mathrm{t}\) and \(m_{B 1}^{c}=9.0 \mathrm{t}\) and \(M_{B 2}=1.0 \mathrm{t}\) and \(m_{B 2}^{c}=0.7 \mathrm{t}\). Both stages of the \(B\) rocket produce the same \(v_{g}\) produced by the engines of the \(A\) rocket. Determine the final velocity of rocket \(A\) when it has exhausted the fuel, and that of rocket \(B\) after exhausting the fuel of the first and second stages. Both rockets start from rest.