Final answer:
Analyzing the movements of the planes and calculating the resulting bearings, will get bearing is 351 degrees.
Step-by-step explanation:
To find the bearing required for the plane to return to the airport, we need to analyze the movements of the plane.
First, the plane travels south 81 degrees east at a speed of 320 mph for 1.5 hours.
This means it covers a distance of 320 * 1.5 = 480 miles in that direction.
Then, the plane makes a 90 degree counterclockwise turn to a new bearing of north 9 degrees east, and travels for 45 minutes.
To find the distance covered in this direction, we use the formula:
distance = speed * time
= 320 * (45/60)
= 240 miles.
Now, we can find the bearing required for the plane to return to the airport.
Since the plane moved south 81 degrees east and then turned counterclockwise by 90 degrees, the new bearing is:
=> 81 + 90 = 171 degrees.
To return to the airport, the plane needs to travel in the opposite direction, so the bearing required is:
=> 171 + 180 = 351 degrees.