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?
To determine the ship's latitude after 45 minutes, we can use the formula:
New Latitude = Initial Latitude + (Change in Latitude per minute * Time in minutes)
The change in the latitude per minute can be found by multiplying the ship's speed (11.6 knots) by the sine of the course (048°). However, since we are given the course as True (T), we need to convert it to Magnetic (M) using the magnetic variation.
Using the magnetic variation at that location, we can add or subtract the corresponding variation to convert the true course to magnetic course. Let's assume the magnetic variation at that location is -2°, which means the True Course (T) will be 048° + (-2°) = 046° (Magnetic).
Now we can calculate the change in latitude per minute:
Change in Latitude per minute = Speed * sine(Course)
= 11.6 * sine(046°)
= 11.6 * 0.7193 (using a calculator to find the sine value)
= 8.31688 (rounded to 5 decimal places)
Now we can calculate the new latitude:
New Latitude = Lat 14°16.2’S + (8.31688 * 45)
= 14°16.2'S + 374.7556
= 14°25.9556'S
Therefore, the ship's latitude after 45 minutes will be approximately Lat 14°25.9556'S.
To determine the latitude of the ship after 45 minutes, we need to calculate the distance it travels in that time at a speed of 11.6 knots.
First, let's convert 45 minutes to hours:
45 minutes = 45/60 = 0.75 hours
Next, we can use the formula: Distance = Speed × Time.
Distance = 11.6 knots × 0.75 hours
= 8.7 nautical miles
Now, we need to calculate the change in latitude using the formula:
Change in Latitude = Distance × Sin(Course)
Since the course is given as 048° (T), we need to convert it to a bearing relative to true north:
Bearing = Course + Variation
Let's assume the variation is 0° for simplicity. Therefore:
Bearing = 048° + 0°
= 048°
Now, we can calculate the change in latitude:
Change in Latitude = 8.7 nautical miles × Sin(048°)
We can use a calculator to find the value of Sin(048°), which is approximately 0.746.
Change in Latitude = 8.7 nautical miles × 0.746
= 6.4852 nautical miles
Finally, we subtract the change in latitude from the initial latitude to find the ship's latitude after 45 minutes:
Latitude after 45 minutes = 14°16.2’ S - 6.4852 nautical miles
= 14°09.7’ S
Therefore, the ship's latitude after 45 minutes is 14°09.7’ S.