The average magnitude of the frictional force due to air drag on the football is -3.15 N.
To find the average magnitude of the frictional force due to air drag, we need to first calculate the acceleration of the football during its flight. We can use the equation of motion: v² = u² + 2ad, where v is the final velocity, u is the initial velocity, a is the acceleration, and d is the distance traveled.
Given that the initial velocity u is 27.7 m/s, the final velocity v is 20.0 m/s, and the distance traveled d is 76.0 m, we can rearrange the equation to solve for acceleration: a = (v² - u²) / (2d).
Substituting the given values, we get: a = (20.0² - 27.7²) / (2 x 76.0) = -3.903 m/s².
The average magnitude of the frictional force due to air drag is equal to the mass of the football multiplied by the acceleration. The mass of the football is 807 g, which is equal to 0.807 kg. Therefore, the average magnitude of the frictional force due to air drag is:
Frictional force = mass x acceleration = 0.807 kg x -3.903 m/s² = -3.15 N.