To find the thrust of the jet engine, we can use the thrust equation based on the conservation of momentum. The thrust can be determined by the momentum change due to the air mass and fuel being consumed and the momentum of the exhaust gases being expelled.
The thrust \( F \) can be calculated using the following formula:
\[ F = \dot{m} \cdot v_{e} + (v_{e} - v_{0}) \cdot \dot{m}_{f} \]
where:
- \( F \) = thrust in Newtons (N)
- \( \dot{m} \) = mass flow rate of air \( (123 , \text{kg/s}) \)
- \( v_{e} \) = velocity of exhaust gases relative to ground
- \( v_{0} \) = velocity of the aircraft relative to ground \( (220 , \text{m/s}) \)
- \( \dot{m}_{f} \) = mass flow rate of fuel \( (1.93 , \text{kg/s}) \) (however, the mass flow rate of fuel does not contribute to thrust under the assumption that the fuel contributes only to combustion, not a separately identifiable thrust component).
First, we calculate the velocity of the exhaust gases relative to the ground \( v_e \):
\[ v_{e} = v_{0} + v_{exhaust} \]
where \( v_{exhaust} \) is the velocity of the exhaust relative to the aircraft \( (925 , \text{m/s}) \):
\[ v_{e} = 220 , \text{m/s} + 925 , \text{m/s} = 1145 , \text{m/s} \]
Next, we can substitute these values into the thrust formula:
\[ F = \dot{m} \cdot v_{e} \] \[ F = 123 , \text{kg/s} \cdot 1145 , \text{m/s} \] \[ F = 140235 , \text{N} \]
Thus, the thrust of the jet engine is
\[ \boxed{140235 , \text{N}} \]
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