$\bullet$ In outer space, where gravity is negligible, a $75,000 \mathrm{kg}$ rocket (including $50,000 \mathrm{kg}$ of fuel) expels this fuel at a steady rate of 135 $\mathrm{kg} / \mathrm{s}$ with a speed of 1200 $\mathrm{m} / \mathrm{s}$ relative to the rocket. (a) Find the thrust of the rocket. (b) What are the initial acceleration and the maximum acceleration of the rocket? (c) After the fuel runs out, what happens to this rocket's acceleration? Does it (i) remain the same as it was just as the fuel ran out, (ii) suddenly become zero, or (iii) gradually drop to zero? Explain your reasoning. (d) After the fuel runs out, what happens to the rocket's speed? Does it (i) remain the same as it was just as the fuel ran out, (ii) suddenly become zero, or (iii) gradually drop to zero? Explain your reasoning.