a) The ship left the port and sailed for 2 hours on a course of 75 degrees,at an average speed of 2.5 nautical miles per hour.

Question

b)
It changed its course to 165 degrees and travelled for 3 hours, at an average speed of 4 nautical miles per hour.

Your team is tasked to lead the rescue. You will be needing the following:
1. distance of the ship from the port
2. bearing from the port to the ship

Answer 1

Disp. = V1*T1 + V2*T2.
Disp. = 2.5[75o]*2 + 4[165o]*4,
Disp. = 5[75o] + 16[165o],
Disp. = (5*Cos75+16*Cos165) + (5*sin75+16*sin165)i,
Disp. = (1.29-15.5) + (4.83+4.14)i,
Disp. = -14.21 + 8.97i = 16.8nM[-32.3o]. = 16.8nM[32.3o N. of W.].

Answer 2

Correction: T2 should 3 hours instead of 4 hours.

Disp. = V1*T1 + V2*T2.
Disp. = 2.5[75o]*2 + 4[165o]*3,
Disp. = 5[75o] + 12[165],
Disp. = (5*Cos75+12*Cos165) + (5*sin75+12*sin165)I,
Disp. = (1.29-15.5) + (4.83+3.11)i,
Disp. = -14.21 + 7.94i = 16.3nM[-29.2o] = 16.3nM[29.2o N. of W.].