Final answer:
To find the mass of the airplane, we can use the concept of lift. The average speed just below the wings is 248 m/s, while it is 275 m/s just above the surface of the wings. Using the equations for lift force and weight, we can calculate the mass of the airplane to be approximately 1088 kg.
Step-by-step explanation:
To find the mass of the airplane, we can use the concept of lift. The average speed just below the wings is 248 m/s, while it is 275 m/s just above the surface of the wings. This difference in speed creates a pressure difference, which results in lift. The lift force can be determined using the equation:
Lift force = (pressure difference) x (wing area)
Given that the pressure difference is the average speed difference, which is 275 m/s - 248 m/s = 27 m/s, and the wing area is 395 m², we can substitute these values into the equation:
Lift force = 27 m/s x 395 m² = 10665 N
The lift force is equal to the weight of the airplane, which can be calculated using the equation:
Weight = mass x gravity
Using the known value of gravity (approximately 9.8 m/s²), we can rearrange the equation to solve for the mass:
mass = Weight / gravity = 10665 N / 9.8 m/s² = 1088 kg
Therefore, the mass of the airplane is approximately 1088 kg.