Final answer:
The air must move over the upper surface of an aircraft's wing at a certain speed at takeoff to generate the necessary lift, according to Bernoulli's principle. This speed is determined by the aircraft's velocity, the air density, and the lift required per square meter of the wing. The required speed changes with different cruising speeds and air densities.
Step-by-step explanation:
The question deals with the scenario of an aircraft at takeoff, which needs to generate enough lift to achieve takeoff speeds. To determine how fast the air must move over the upper surface of the wing, we can apply Bernoulli's principle. The principle suggests that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Given that the aircraft is traveling at 60.0 m/s at takeoff, and considering the air's density to be 1.29 kg/m³, we can use the lift equation and Bernoulli's equation to find out the required speed over the top surface for generating the needed 1000 N of lift per square meter of wing.
Similarly, the calculation would change for an aircraft at cruising speed, where the air density is one-fourth that at sea level. The dynamic pressure on the wing will change, requiring a different speed of air over the upper surface to maintain the same lift.