A rocket sled with initial mass of \(900 \mathrm{~kg}\) is to be accelerated on a level track. The rocket motor burns fuel at constant rate \(\dot{m}=13.5 \mathrm{~kg} / \mathrm{s}\). The rocket exhaust flow is uniform and axial. Gases leave the nozzle at \(2750 \mathrm{~m} / \mathrm{s}\) relative to the nozzle, and the pressure is atmospheric. Determine the minimum mass of rocket fuel needed to propel the sled to a speed of \(265 \mathrm{~m} / \mathrm{s}\) before burnout occurs. As a first approximation, neglect resistance forces.