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.
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
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.].
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.].
To find the distance of the ship from the port, we can use the concept of trigonometry and the information given about the ship's course and average speed.
a) In the first part, the ship sailed for 2 hours on a course of 75 degrees at an average speed of 2.5 nautical miles per hour. To find the distance traveled, we can use the formula:
Distance = Speed * Time
Distance = 2.5 nautical miles per hour * 2 hours = 5 nautical miles
b) In the second part, the ship changed its course to 165 degrees and traveled for 3 hours at an average speed of 4 nautical miles per hour. Again, using the formula:
Distance = Speed * Time
Distance = 4 nautical miles per hour * 3 hours = 12 nautical miles
Now, to find the total distance of the ship from the port, we can add the distances from part a) and part b):
Total Distance = Distance from part a) + Distance from part b)
= 5 nautical miles + 12 nautical miles
= 17 nautical miles
So, the distance of the ship from the port is 17 nautical miles.
Next, to find the bearing from the port to the ship, we can use the concept of trigonometry.
In part a), the ship sailed on a course of 75 degrees, which means the angle between the ship's course and a line from the ship to the port is 75 degrees.
In part b), the ship changed its course to 165 degrees, which means the angle between the ship's course and a line from the ship to the port is 165 degrees.
To find the bearing from the port to the ship, we can add these two angles together:
Bearing = 75 degrees + 165 degrees
= 240 degrees
So, the bearing from the port to the ship is 240 degrees.