Final answer:
The remaining mass of the rocket after fuel burning for 250 seconds is 2.43 × 10⁵ kg, which is the initial rocket mass minus the consumed fuel mass.
Step-by-step explanation:
When the rocket engine is turned off after burning fuel for 250 seconds at a rate of 480 kg/s, we can find the weight of the remaining fuel (and hence the total weight of the rocket) by considering the initial mass of the fuel and subtracting the mass of the fuel that has been consumed.
The initial mass of the fuel is given as 1.81 × 10⁵ kg. The rate of consumption is 480 kg/s, for a duration of 250 seconds. So the total fuel consumed is:
Consumed fuel = consumption rate × duration = 480 kg/s × 250 s = 120,000 kg
Subtracting this from the initial fuel mass:
Remaining fuel mass = initial fuel mass - consumed fuel = (1.81 × 10⁵ kg) - 120,000 kg = 1.69 × 10⁵ kg
The total mass of the rocket after burning fuel is thus the sum of the mass of the rocket without fuel (given as 2.55 × 10⁵ kg) and the remaining fuel mass:
Total rocket mass after fuel burning = (2.55 × 10⁵ kg) - (1.81 × 10⁵ kg - 1.69 × 10⁵ kg) = 2.43 × 10⁵ kg.