Final answer:
By considering the 2-minute safety interval between takeoffs, the run time on the runway, and the average waiting time before takeoff, we calculated the number of planes either on the runway or waiting to take off. The calculation shows that there will typically be one plane on the runway and approximately 13 planes either on the runway or waiting to take off within an hour.
Step-by-step explanation:
To determine the number of planes either on the runway or waiting to take off, we need to use the given information about the frequency of takeoffs and the waiting time. According to the safety regulations, there must be a minimum of 2 minutes between each takeoff. Given that 14 planes take off per hour, we can break down one hour into 60 minutes to determine how many planes can theoretically take off in that time frame. However, the practical waiting time to take off is 3 minutes and 57 seconds for each plane.
To find the total time per cycle (for a plane to take off and the runway to be clear for the next plane), we add the run time on the runway (33 seconds) to the waiting time (3 minutes and 57 seconds). This gives us 4 minutes and 30 seconds per cycle. Since we have 60 minutes in an hour, and each plane requires 4 minutes and 30 seconds per cycle, we can divide:
60 minutes / 4.5 minutes = 13.33 cycles
This implies that approximately 13 planes can complete the cycle of taking off in one hour. Given that 14 planes are taking off per hour, there will usually be one plane on the runway and approximately 13 planes either on the runway or waiting in line to take off within the hour.