Question
A ship sails for 5 hours from position A: (27° 38' N, 112° 45' W) at a speed of 16 knots on a course of 295°T.
Answers
GPT 3.5
To determine the new position after 5 hours, we need to calculate the distance traveled by the ship using the formula:
distance = speed * time
Given that the speed is 16 knots and the time is 5 hours, we have:
distance = 16 knots * 5 hours
distance = 80 nautical miles
To calculate the new latitude and longitude coordinates, we need to use the course angle of 295°T. First, we need to convert the angle to radians by multiplying it by π/180:
295° * π/180 = 5.1488 radians
Next, we use the haversine formula to calculate the change in latitude and longitude:
change in latitude = distance * sin(course angle)
change in longitude = distance * cos(course angle)
Given that the distance is 80 nautical miles, we have:
change in latitude = 80 nm * sin(5.1488 radians)
change in longitude = 80 nm * cos(5.1488 radians)
Using a reference website or mathematical tool, we can calculate that:
sin(5.1488 radians) ≈ 0.08906
cos(5.1488 radians) ≈ 0.99601
Therefore, the change in latitude is approximately:
change in latitude ≈ 80 nm * 0.08906
change in latitude ≈ 7.12448 nm
And the change in longitude is approximately:
change in longitude ≈ 80 nm * 0.99601
change in longitude ≈ 79.6808 nm
To find the new latitude and longitude coordinates, we add the change in latitude and longitude to the initial coordinates:
New latitude = 27° 38' N + 7.12448 nm ≈ 27° 45' N
New longitude = 112° 45' W + 79.6808 nm ≈ 112° 53' W
Therefore, the new position after 5 hours of sailing at a speed of 16 knots on a course of 295°T is approximately (27° 45' N, 112° 53' W).
distance = speed * time
Given that the speed is 16 knots and the time is 5 hours, we have:
distance = 16 knots * 5 hours
distance = 80 nautical miles
To calculate the new latitude and longitude coordinates, we need to use the course angle of 295°T. First, we need to convert the angle to radians by multiplying it by π/180:
295° * π/180 = 5.1488 radians
Next, we use the haversine formula to calculate the change in latitude and longitude:
change in latitude = distance * sin(course angle)
change in longitude = distance * cos(course angle)
Given that the distance is 80 nautical miles, we have:
change in latitude = 80 nm * sin(5.1488 radians)
change in longitude = 80 nm * cos(5.1488 radians)
Using a reference website or mathematical tool, we can calculate that:
sin(5.1488 radians) ≈ 0.08906
cos(5.1488 radians) ≈ 0.99601
Therefore, the change in latitude is approximately:
change in latitude ≈ 80 nm * 0.08906
change in latitude ≈ 7.12448 nm
And the change in longitude is approximately:
change in longitude ≈ 80 nm * 0.99601
change in longitude ≈ 79.6808 nm
To find the new latitude and longitude coordinates, we add the change in latitude and longitude to the initial coordinates:
New latitude = 27° 38' N + 7.12448 nm ≈ 27° 45' N
New longitude = 112° 45' W + 79.6808 nm ≈ 112° 53' W
Therefore, the new position after 5 hours of sailing at a speed of 16 knots on a course of 295°T is approximately (27° 45' N, 112° 53' W).