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.
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).
To determine the final position of the ship, we'll first need to calculate the distance travelled using the speed and time. We'll then calculate the change in latitude and longitude based on the course.
Step 1: Calculate the distance travelled.
Distance = Speed x Time
Distance = 16 knots x 5 hours
Distance = 80 nautical miles
Step 2: Calculate the change in latitude.
Latitude is measured in degrees, and the distance travelled is given in nautical miles. To convert nautical miles to degrees, we'll use the conversion factor of 1 nautical mile = 1 minute of latitude.
Change in Latitude = Distance / Conversion Factor
Change in Latitude = 80 nautical miles / 1 minute of latitude
Conversion Factor:
1 nautical mile = 1 minute of latitude
1 degree = 60 minutes of latitude
Change in Latitude = 80 nautical miles / (1/60)
Change in Latitude = 80 x 60
Change in Latitude = 4800 minutes of latitude
Step 3: Calculate the change in longitude.
Longitude is measured in degrees, and the change in longitude will depend on the course. To calculate the change in longitude, we'll need to convert nautical miles to degrees using the conversion factor for the specific latitude.
Conversion Factor for Longitude:
1 nautical mile = 1 minute of longitude
1 minute of longitude = 1 nautical mile x cos(latitude)
Latitude at position A: 27° 38' N
Change in Longitude = Distance / Conversion Factor
Change in Longitude = 80 nautical miles / (1/60) x cos(27° 38')
Step 4: Convert the latitude and longitude changes to the proper format.
Latitude at position A: 27° 38' N
Change in Latitude: 4800 minutes of latitude / 60 = 80 degrees
Longitude at position A: 112° 45' W
Change in Longitude: Calculate based on the conversion factor derived from latitude
Finally, add the changes in latitude and longitude to the initial position to get the final position.