Taking into account the weight loss of fuel, the maximum velocity v_m of a rocket is v_m = u(ln m₀ − ln m_s) − gt_f, where m₀ is the initial mass of the rocket and fuel, ms is the mass of the rocket shell, tf is the time during which fuel is expended, u is the velocity of the expelled fuel, and g is the acceleration due to gravity. Solve for m₀.