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A jet aircraft is traveling at 260 m/s in horizontal flight. The engine takes in air at a rate of 53.3 kg/s and burns fuel at a rate of 3.63 kg/s. The exhaust gases are ejected at 317 m/s relative to the aircraft. Find the thrust of the jet engine. Answer in units of N.

Respuesta :

Answer:

The thrust of the jet engine is 4188.81 N.

Explanation:

Given that,

Speed = 260 m/s

Rate in air= 53.3 kg/s

Rate of fuel = 3.63 kg/s

Relative speed = 317 m/s

We need to calculate the rate of mass change in the rocket

Using formula of rate of mass

[tex]\dfrac{dM}{dt}=\dfrac{dM_{a}}{dt}+\dfrac{dM_{f}}{dt}[/tex]

Put the value into the formula

[tex]\dfrac{dM}{dt}=53.3+3.63[/tex]

[tex]\dfrac{dM}{dt}=56.93\ kg/s[/tex]

We need to calculate the thrust of the jet engine

Using formula of thrust

[tex]T=\dfrac{dM}{dt}u-\dfrac{dM_{a}}{dt}v[/tex]

Put the value into the formula

[tex]T=56.93\times317-53.3\times260[/tex]

[tex]T=4188.81\ N[/tex]

Hence, The thrust of the jet engine is 4188.81 N.

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