To determine the magnitude of the horizontal thrust generated by the airplane's propeller, we need to consider the total mass being accelerated and the acceleration.
Step 1: Calculate the total mass being accelerated.
The total mass \( m_{total} \) is the sum of the mass of the airplane and the masses of the gliders:
\[ m_{total} = m_{plane} + m_{glider1} + m_{glider2} \]
Where:
- \( m_{plane} = 2200 , \text{kg} \)
- \( m_{glider1} = 350 , \text{kg} \)
- \( m_{glider2} = 250 , \text{kg} \)
Calculating \( m_{total} \):
\[ m_{total} = 2200 , \text{kg} + 350 , \text{kg} + 250 , \text{kg} = 2800 , \text{kg} \]
Step 2: Calculate the total force required to accelerate the entire system.
Using Newton's second law:
\[ F = m \cdot a \]
Where:
- \( F \) is the total force (thrust in this case),
- \( m \) is the total mass (2800 kg),
- \( a \) is the acceleration (1.3 m/s²).
Calculating the total thrust:
\[ F = 2800 , \text{kg} \cdot 1.3 , \text{m/s}^2 = 3640 , \text{N} \]
Conclusion
The magnitude of the horizontal thrust of the plane's propeller is \( \mathbf{3640 , N} \).