Discussion
A rocket has an initial mass of 150 kg. After operating for a duration of 10 s, its final mass is 50 kg. If the acceleration due to gravity is 9.81 m/s2 and the thrust produced by the rocket is 19.62 kN, the specific impulse of the rocket is
Answer: C
The specific impulse is 200 s.
The rocket burns \(150 - 50 = 100\) kg of propellant in 10 s, a mass flow of 10 kg/s. Specific impulse is thrust per unit weight flow of propellant:
\[ \begin{aligned} I_{sp} &= \frac{F}{\dot{m}g} \\ &= \frac{19620}{10 \times 9.81} = 200\ \text{s} \end{aligned} \]
400 s would need a mass flow of only 5 kg/s, half the actual figure, and 100 s would need 20 kg/s. 300 s corresponds to about 6.7 kg/s, which is what dividing the 100 kg burnt by 15 s instead of 10 s would give. Only 10 kg/s matches the stated masses and burn time.
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