Question

A solid propellant rocket producing 25 MN thrust is fired for 150 seconds. The specific impulse of the rocket is 2980 Ns/kg. How much propellant is burned during the rocket operation?

• A. 8390 kg
• B. 82300 kg
• C. $1.26 \times 10^6$ kg
• D. $11.2 \times 10^6$ kg

Hint:

Always use $m = \frac{F}{I_s} \times t$ for total propellant used in rockets with constant thrust.

Answer 1

The Correct Option is C

We are given:
Thrust: \(F = 25 \times 10^6\ \text{N}\)
Burn time: \(t = 150\ \text{s}\)
Specific impulse: \(I_s = 2980\ \text{Ns/kg}\)
1. Understanding specific impulse:
Specific impulse relates thrust to mass flow rate: \[ I_s = \frac{F}{\dot{m}} $\Rightarrow$ \dot{m} = \frac{F}{I_s} \] 2. Compute mass flow rate:
\[ \dot{m} = \frac{25 \times 10^6}{2980} \approx 8390\ \text{kg/s} \] 3. Compute total propellant consumed:
\[ m = \dot{m} \times t = 8390 \times 150 \] \[ m \approx 1.26 \times 10^6\ \text{kg} \] This is approximately 1.26 million kilograms of solid propellant burned in 150 seconds. The large value is consistent with typical heavy-lift booster rockets.