Final answer:
The magnitude of the acceleration of the pilot at the lowest point in a vertical dive, with a constant airplane speed of 300 km/h and a radius of 0.58 km, is approximately 11.97 m/s². This is the centripetal acceleration experienced by the pilot.
Step-by-step explanation:
The student is asking about the magnitude of acceleration experienced by a pilot at the lowest point of a vertical dive, given that the airplane has a constant speed of 300 km/h and is performing a circular motion with a radius of 0.58 km. To find the acceleration, we need to use the formula for centripetal acceleration, which is a = v^2/r where v is the speed and r is the radius of the circular path.
First, we need to convert the speed to meters per second (m/s) since we want the acceleration in meters per second squared (m/s2). 300 km/h is equivalent to 83.33 m/s (1 km/h is approximately 0.27778 m/s). Next, the radius is already given in kilometers, so we must convert it to meters: 0.58 km is 580 meters.
Using the formula a = v^2/r, we calculate the acceleration as follows:
a = (83.33 m/s)^2 / 580 m, which equals approximately 11.97 m/s2. This is the centripetal acceleration that the pilot feels towards the center of the circular path at the lowest point of the dive.