Final answer:
The centripetal acceleration of the plane is approximately 6.28 m/s²
Step-by-step explanation:
The centripetal acceleration of an object moving in a circular path can be calculated using the formula ac = v^2 / r, where v is the speed of the object and r is the radius of the path. In this case, the speed of the plane is not given, but we are given the time it takes to complete one circle and the radius of the path.
We can solve for the speed of the plane by dividing the circumference of the circular path by the time taken: v = 2πr / t. Plugging in the values, we get v = 2π(4000) / 30. Once we have the speed, we can calculate the centripetal acceleration using the formula mentioned earlier: ac = v^2 / r.
Calculating the value, we get ac = (2π(4000) / 30)^2 / 4000, which simplifies to ac ≈ 6.28 m/s².