A rocket has an initial mass of 30,000 kg, of which 20% is the payload. It burns fuel at a rate of 200 kg/s and exhausts its gas at a relative speed of 1.8 km/s. Find

(a) The thrust of the rocket,

(b) The time until burnout, and

(c) Its final speed assuming it moves upward near the surface of the earth where the gravitational field g is constant.