Final answer:
The power developed by the airplane engine flying at 250 m/s with a thrust of 10,000 N is approximately 2,500,000 W or 3352.8 hp.
Step-by-step explanation:
To calculate the power developed by the airplane engine in horsepower, we use the formula for power when force and velocity are known:
Power (P) = Force (F) × Velocity (v)
Where the thrust (force) is 10,000 N and the velocity of the airplane is 250 m/s. Inserting these values gives us:
P = 10,000 N × 250 m/s = 2,500,000 W (watts)
To convert this power into horsepower (hp), we use the fact that 1 horsepower is equivalent to 746 watts.
Power in horsepower = Power in watts / 746
Power in horsepower = 2,500,000 W / 746 ≈ 3352.8 hp