Final answer:
The approximate force on a square meter of sail can be calculated using Bernoulli's principle. The force is approximately 45.4 N and is great enough to be effective for propelling a sailboat.
Step-by-step explanation:
To calculate the approximate force on a square meter of sail, we can use Bernoulli's principle.
Bernoulli's principle states that as the wind moves across the sail, the air pressure decreases.
This pressure difference creates a net force on the sail. The net force is equal to the product of the pressure difference and the area of the sail.
Given that the horizontal velocity of the wind is 6.00 m/s parallel to the front surface and 3.50 m/s along the back surface, we need to calculate the pressure difference between the front and back surfaces of the sail.
The pressure difference can be calculated using the equation:
Pressure difference = 0.5 * density of air * (velocity of wind on front surface squared - velocity of wind on back surface squared)
Substituting the given values, we get:
Pressure difference = 0.5 * 1.29 kg/m³ * (6.00 m/s)^2 - (3.50 m/s)^2 = 45.4 N
Therefore, the approximate force on a square meter of sail is approximately 45.4 N.
The force is great enough to be effective for propelling a sailboat, as it provides a significant amount of propulsion that can be used to move the boat through the water.