Question

A stunt pilot of mass 48.0 kg who has been diving her airplane vertically pulls out of the dive by changing her course to a circle in a vertical plane. If the plane's speed at the lowest point of the circle is 95.2 m/s, what is the minimum radius of the circle for the acceleration at this point not to exceed 4.00 g?

Answer 1

The minimum radius of the circle that the stunt pilot must follow to ensure the acceleration does not exceed 4g is approximately 231.04 meters, calculated using the centripetal acceleration formula with given velocity and acceleration values.

Step-by-step explanation:

The question pertains to calculating the minimum radius of the circle that the stunt pilot must follow in a vertical plane so that the acceleration does not exceed 4 times the acceleration due to gravity (4g). Given the pilot's speed at the lowest point, we can relate the acceleration to the velocity and radius of the circular path using the centripetal acceleration formula a = v²/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular path.

Let's calculate the minimum radius needed to not exceed 4g. Since 1g is approximately 9.81 m/s², 4g would be 4 × 9.81 m/s². We have the velocity of the plane, v = 95.2 m/s, and the maximum centripetal acceleration allowed, a = 4g. The radius can be calculated as follows:

r = v² / a
r = (95.2 m/s)² / (4 × 9.81 m/s²)
r ≈ 231.04 m

Therefore, the minimum radius of the circle that the stunt pilot must follow is approximately 231.04 meters.