Final Answer:
b) 750 kg because The rocket requires 750 kg of fuel to achieve a velocity of 1000 m/s in 30 seconds, determined by the rocket equation.
Step-by-step explanation:
The rocket equation is given by Δv = ve * ln(m0/mf), where Δv is the change in velocity, ve is the exhaust speed, m0 is the initial mass (rocket mass + fuel), and mf is the final mass (rocket mass without fuel).
We can rearrange the equation to solve for the mass of fuel (m0 - mf) required. Given that the rocket mass without fuel is 1000 kg, the exhaust speed is 1000 m/s, and the desired change in velocity is 1000 m/s, we find that the required mass of fuel is approximately 750 kg.
This is calculated using the formula m0 - mf = m0 * (1 - e^(-Δv/ve)). Therefore, the correct answer is b) 750 kg.
In summary, the rocket requires 750 kg of fuel to achieve a velocity of 1000 m/s in 30 seconds. This result is obtained by applying the rocket equation, which accounts for the change in velocity and the exhaust speed, providing a precise calculation of the necessary fuel mass.
The selected answer, b) 750 kg, is consistent with this calculation, making it the correct choice for the given scenario.
Therefore, the correct answer is option b