Question

A jet aircraft is traveling at 200 m/s in horizontal flight. The engine takes in air at a rate of 47.5 kg/s and burns fuel at a rate of 2.51 kg/s. The exhaust gases are ejected at 498 m/s relative to the aircraft. Find the thrust of the jet engine.

Answer 1

The thrust of the jet engine is calculated using the conservation of momentum and Newton's third law of motion, yielding a force of 14210 Newtons.

Step-by-step explanation:

The question involves calculating the thrust of a jet engine using principles from physics, specifically the conservation of momentum and Newton's third law of motion. We know the velocity of the jet (200 m/s), the rate at which air is taken in (47.5 kg/s), the rate at which fuel is burned (2.51 kg/s), and the velocity of the exhaust gases (498 m/s relative to the aircraft).

To calculate the thrust, we can use the formula: Thrust = (rate of mass flow of exhaust gases * exhaust velocity) - (rate of mass flow of intake air * intake air velocity). Since it's horizontal flight, the intake air velocity is the same as the velocity of the jet (200 m/s). So, we'll have:
Thrust = (47.5 kg/s * 498 m/s) - (47.5 kg/s * 200 m/s)
= 23710 N - 9500 N
= 14210 N

Therefore, the thrust generated by the jet engine is 14210 Newtons (N).