A ship sails from Lat 14°16.2’S with a course of 048° (T) with a speed of 11.6 knots. What is her latitude after 45 minutes?
Distance= Dlat/Cos Course
Distance= Speed x time
Distance = Speed x time
Distance = 11.6 knots x 45 minutes
Since 1 knot = 1 nautical mile per hour,
Distance = 11.6 nautical miles/hour x 45 minutes
Distance = 11.6/60 nautical miles/minute x 45 minutes
Distance = 0.1933 nautical miles/minute x 45 minutes
Distance = 8.6995 nautical miles
To find the change in latitude, we use the formula:
Change in latitude = Distance / (60 nautical miles/degree)
Change in latitude = 8.6995 nautical miles / (60 nautical miles/degree)
Change in latitude = 0.14499 degrees
Since the ship sails from Latitude 14°16.2'S, the final latitude will be:
Latitude = Initial Latitude - Change in latitude
Latitude = 14°16.2' S - 0.14499°
The final latitude after 45 minutes is approximately 14°15.46' S.
To find the ship's latitude after 45 minutes, we first need to calculate the distance it has traveled.
1. Convert the speed from knots to nautical miles per minute:
Speed = 11.6 knots = 11.6 nautical miles per hour
Since there are 60 minutes in an hour, the speed in nautical miles per minute is:
Speed = 11.6 nautical miles per hour / 60 = 0.1933 nautical miles per minute
2. Calculate the distance traveled in 45 minutes:
Distance = Speed x time
Distance = 0.1933 nautical miles per minute x 45 minutes = 8.6996 nautical miles
3. Calculate the change in latitude:
Change in Latitude = Distance / Cos(Course)
The cosine of the course angle (48° True) can be calculated using a scientific calculator or trigonometric tables.
4. Calculate the final latitude:
Final Latitude = Initial Latitude - Change in Latitude
Since the initial latitude is given as 14°16.2'S, we need to convert it to decimal degrees.
Converting 16.2 minutes to decimal degrees:
16.2 minutes / 60 = 0.27 degrees
Initial Latitude in decimal degrees = 14 degrees + 0.27 degrees = 14.27 degrees
Plug in the values to calculate the change in latitude:
Change in Latitude = 8.6996 nautical miles / Cos(48° True)
Plug in the values to calculate the final latitude:
Final Latitude = 14.27 degrees - Change in Latitude
Please note that to obtain the exact value, the cosine value should be calculated using a scientific calculator or trigonometric tables.