A) To calculate the speed of the plane, we can use the formula for centripetal acceleration:
a = v^2 / r
where a is the centripetal acceleration, v is the speed of the plane, and r is the radius of the circular path.
We are given that the centripetal acceleration is 1g, which is equal to 9.8 m/s^2. We are also given the radius of the circular path as 200 m.
Substituting these values into the formula, we get:
9.8 m/s^2 = v^2 / 200 m
Solving for v, we get:
v = √(9.8 m/s^2 * 200 m) ≈ 44.2 m/s
Therefore, the speed of the plane is approximately 44.2 m/s.
B) To calculate the time required to make the turn, we can use the formula for the period of a uniform circular motion:
T = 2πr / v
where T is the period, r is the radius, and v is the speed of the object in uniform circular motion.
Substituting the given values, we get:
T = 2π(200 m) / (44.2 m/s) ≈ 28.6 s
Therefore, the time required to make the turn is approximately 28.6 seconds.