Final answer:
The acceleration of a 5000-kg rocket taking off from the Moon, calculated using the thrust produced by the expelled gas and the weight of the rocket on the Moon, is 33.6 m/s².
Step-by-step explanation:
To calculate the acceleration of the rocket during its launch on the Moon, we can use the principles of physics specifically Newton's second law (force equals mass times acceleration) and the concept of thrust generated by the expulsion of gas.
First, let's determine the thrust (force) the rocket produces:
- Thrust = mass of gas expelled per second × exhaust velocity of gas
- Thrust = 8.00 kg/s × 2.20×10³ m/s = 1.76×10µ N
With the thrust known, we can now calculate the rocket's acceleration as follows:
- Net force = thrust - weight of the rocket
- Weight of the rocket on the Moon = mass of the rocket × acceleration due to Moon's gravity
- Weight of the rocket on the Moon = 5000 kg × 1.6 m/s² = 8000 N
- Net force = 1.76×10µ N - 8000 N = 1.68×10µ N
- Acceleration = net force / mass of the rocket
- Acceleration = 1.68×10µ N / 5000 kg = 33.6 m/s²
So, the acceleration of the rocket during its initial 16 seconds of launch on the Moon is 33.6 m/s².