Question

An airplane is flying in a horizontal circle at a speed of 82.4 m/s. The 50.2 kg pilot does not want his radial acceleration to exceed 5.36 g. The acceleration of gravity is 9.8 m/s2. What is the minimum radius of the circular path? Answer in units of m

a. What is the speed of the airplane?

Answer 1

The minimum radius of the circular path for the airplane to ensure the pilot's radial acceleration does not exceed 5.36g, given a speed of 82.4 m/s, is approximately 126.377 meters.

Step-by-step explanation:

The question asks for the minimum radius of the circular path an airplane must fly in so that the radial (centripetal) acceleration experienced by the pilot does not exceed 5.36 times the acceleration due to gravity, given that the speed of the airplane is 82.4 m/s. To solve this, we use the formula for centripetal acceleration (a = v^2/r), where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular path.

The maximum centripetal acceleration allowable is 5.36g, with g being 9.8 m/s2. Hence, 5.36g equals 5.36 × 9.8 m/s2. Setting up the equation:

5.36 × 9.8 m/s2 = (82.4 m/s)2 / r

So, r = (82.4 m/s)2 / (5.36 × 9.8 m/s2)

After calculating, the minimum radius is found to be r = 126.377 m approximately.