Answer :
Final Answer:
The initial mass of the rocket if the exhaust speed is 1,330 m/s and the mass of fuel burned is 101 kg was approximately 2,911 kg.
Explanation:
To find the initial mass of the rocket, we can use the rocket equation, which relates the change in velocity (Δv), the exhaust speed (Ve), the mass of the rocket with fuel (M), and the mass of the burned fuel (m):
Δv = Ve * ln(M0 / M)
Where:
Δv = Change in velocity (266 m/s)
Ve = Exhaust speed (1,330 m/s)
M0 = Initial mass of the rocket (unknown)
M = Final mass of the rocket (M0 - m, where m is the mass of fuel burned, 101 kg)
We have the values for Δv, Ve, and m, and we want to find M0. Rearrange the equation to solve for M0:
M0 = M * e^(Δv / Ve)
M0 = (M - m) * e^(Δv / Ve)
M0 = (M - 101 kg) * e^(266 m/s / 1,330 m/s)
M0 ≈ 2,911 kg
So, the initial mass of the rocket was approximately 2,911 kg.
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