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A jet aircraft is traveling at 202 m/s in horizontal flight. The engine takes in air at a rate of 35.2 kg/s and burns fuel at a rate of 2.35 kg/s. The exhaust gases are ejected at 924 m/s relative to the aircraft. Find the thrust of the jet engine. Answer in units of N.

A) 17,340 N

B) 32,864 N

C) 19,604 N

D) 23,616 N

User ISQ
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1 Answer

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Final answer:

The thrust of the jet engine is calculated using conservation of momentum, considering the mass flow rate of air and fuel and the exhaust gases' ejection speed. However, none of the options given match the calculated thrust of 27598 N, so there might be an error in the question parameters or options.

Step-by-step explanation:

To calculate the thrust of the jet engine, we can use the principle of conservation of momentum. The mass flow rate of the exhaust gases, the relative speed of the exhaust gases, and the fuel consumption all play roles in determining the force that the engine generates.

The thrust (F) can be found using the formula:
F = Δ(mv) / Δt
where:
Δ(mv) is the change in momentum,
Δt is the change in time.

The change in momentum includes both the mass of the fuel being burned and the air being taken in. Therefore:
F = ((mair + mfuel) × vexhaust - mair × vaircraft) / Δt

Given that mair = 35.2 kg/s,
mfuel = 2.35 kg/s,
vexhaust = 924 m/s,
and vaircraft = 202 m/s,
the calculation for thrust will be as follows:

F = ((35.2 kg/s + 2.35 kg/s) × 924 m/s - 35.2 kg/s × 202 m/s) / 1 s

This simplifies to:

F = (37.55 kg/s × 924 m/s - 35.2 kg/s × 202 m/s) / 1 s

F = (34702 - 7104) N/s
F = 27598 N

Considering the provided options for the thrust, none of them match the calculated value. Please check the question parameters or the possible answers for any discrepancies.

User Concat
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