Final answer:
a) The latitude at midday is 138.2 degrees South.
b) The plane passes over the South Pole at approximately 10 a.m. 2.7 minutes.
Step-by-step explanation:
a) To determine the latitude at midday, we need to calculate the distance the plane has flown in 2 hours.
Since the plane is flying due South at a steady speed of 800 km/h, it will cover a distance of 1600 km in 2 hours.
Therefore, the latitude at midday is 54 degrees South minus 1600 km, which gives the new latitude as 54 - 1600 = 138.2 degrees South.
b) To find the time the plane passes over the South Pole, we can first calculate the distance it needs to fly to reach the South Pole.
The South Pole is located at latitude 90 degrees South, so the plane needs to fly a distance of 90 - 54 = 36 degrees of latitude.
Since the plane is flying at a speed of 800 km/h, it will take it 36 / 800 = 0.045 hours to reach the South Pole.
Converting this to minutes, we have 0.045 * 60 = 2.7 minutes.
Therefore, the plane will pass over the South Pole at 10 a.m. + 2.7 minutes, which is approximately 10 a.m. 2.7 minutes.