Question

PART ONE

A jet aircraft is traveling at 281 m/s in horizontal flight. The engine takes in air at a
rate of 107 kg/s and burns fuel at a rate of
4.23 kg/s. The exhaust gases are ejected at
679 m/s relative to the aircraft.
Find the thrust of the jet engine.
Answer in units of N.

PART TWO
Find the delivered power.
Answer in units of W

Answer 1

1. F = 45,458.17 N

2. P = 12,800,000 W

Step-by-step explanation:

Part 1. The thrust force is the sum of the forces on the air and on the fuel.

For the air, 107 kg of air is accelerated from 281 m/s to 679 m/s in 1 second.

F = ma

F = (107 kg) (679 m/s − 281 m/s) / (1 s)

F = 42,586 N

For the fuel, 4.23 kg of fuel is accelerated from 0 m/s to 679 m/s in 1 second.

F = ma

F = (4.23 kg) (679 m/s − 0 m/s) / (1 s)

F = 2,872.17 N

So the thrust on the jet is:

F = 42,586 N + 2,872.17 N

F = 45,458.17 N

Rounded to three significant figures, the force is 45,500 N.

Part 2. Power = work / time, and work = force × distance, so:

Power = force × distance / time

Power = force × velocity

P = (45,458.17 N) (281 m/s)

P = 12,773,745.77 W

Rounded to three significant figures, the power is 12,800,000 W.