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.

Find the departure, DEP, for the final position.

Answer 1

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.