An aircraft departing A(N40° 00′ E080° 00′) flies a constant true track of 270° at a ground speed of 120 kt. What are the coordinates of the position reached in 6 HR?

Steps to Solve

1. Calculate the Distance Traveled The first step is to determine how far the aircraft travels in 6 hours at a speed of 120 knots. To find the distance, we use the formula: $$ \text{Distance} = \text{Speed} \times \text{Time} $$

Substituting in the values: $$ \text{Distance} = 120 , \text{knots} \times 6 , \text{hours} = 720 , \text{nautical miles} $$

2. Determine the Track Direction The aircraft is flying at a true track of 270°, which means it is heading directly west. This affects how we calculate the change in coordinates.

3. Convert Distance to Latitude/Longitude Change To find out how this distance affects the coordinates, we need to convert nautical miles to degrees of latitude and longitude.

• The latitude (north-south) changes approximately by 1 nautical mile = 1/60 degrees.
• The longitude (east-west) changes approximately by 1 nautical mile = 1/60 degrees at the equator, but we need to apply the cosine of the latitude for correct conversion at higher latitudes.

For this problem:

• Since the aircraft stays at the same latitude (N40°), we only need to adjust longitude.

The change in longitude: $$ \text{Change in Longitude} = \frac{720 , \text{nautical miles}}{60} , \text{degrees} = 12 , \text{degrees} $$

4. Adjust the Initial Coordinates The initial coordinates are N40°00' E80°00'. Since the aircraft is traveling west, we subtract the change in longitude: $$ \text{New Longitude} = 80°00' - 12° = 68°00' $$

Thus, the new coordinates are: $$ \text{New Position} = N40°00' E68°00' $$

5. Determine Final Coordinates in Options Now we will compare the calculated position with the provided options to find the match.