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.
Find the departure, DEP, for the final position.
To find the departure (DEP) for the final position, we need to use the formula:
DEP = sin(coordinate of distance traveled) * speed
First, let's convert the coordinates of position A from degrees, minutes, and seconds to decimal degrees.
27° 38' N = 27 + (38/60) = 27.6333° N
112° 45' W = -112 - (45/60) = -112.75° W
Given that the course is 295°T, we need to convert it to a decimal course bearing. The conversion is as follows:
T = True course
M = Magnetic variation
C = Compass course
T = M + C
The magnetic variation is the angle between true north and magnetic north at a particular location. Let's assume the magnetic variation is 10°E.
T = 295°T
M = 10°E
C = T - M
C = 295°T - 10°E = 285°
Now, let's calculate the departure for the final position:
DEP = sin(distance traveled) * speed
The distance traveled can be calculated using the formula:
Distance traveled = speed * time
Given that the speed is 16 knots and the time is 5 hours:
Distance traveled = 16 knots * 5 hours = 80 nautical miles
Now, let's calculate the departure:
DEP = sin(285°) * 80
Using a scientific calculator:
DEP = sin(285°) * 80 = -0.9330 * 80 = -74.64
Therefore, the departure (DEP) for the final position is approximately -74.64 nautical miles.
To find the departure (DEP) for the final position, we need to calculate the distance traveled by the ship from position A.
Given:
Position A: 27° 38' N, 112° 45' W
Speed: 16 knots
Course: 295°T
Time: 5 hours
First, we need to convert the coordinates from degrees and minutes to decimal degrees.
Latitude of position A (27° 38' N):
27 + (38/60) = 27.6333 degrees N
Longitude of position A (112° 45' W):
-112 - (45/60) = -112.75 degrees W
Next, we can use the formula for distance, speed, and time:
Distance = Speed × Time
Distance = 16 knots × 5 hours
Distance = 80 nautical miles
Now, we can calculate the departure (DEP) for the final position:
DEP = Distance × sin(course)
DEP = 80 nautical miles × sin(295°T)
To use the trigonometric function sin, we need to convert the course from True (T) to Magnetic (M) using the magnetic variation for the location.
Let's assume the magnetic variation for the location is 10°E. Therefore, the magnetic course (M) is:
Magnetic Course (M) = True Course (T) + Magnetic Variation (V)
Magnetic Course (M) = 295°T + 10°E (east variation)
Magnetic Course (M) = 305°M
Now, we can calculate the departure (DEP):
DEP = 80 nautical miles × sin(305°M)
Using a calculator, we find that sin(305°) = -0.5.
DEP = 80 nautical miles × (-0.5)
DEP = -40 nautical miles
Therefore, the departure (DEP) for the final position is -40 nautical miles.