A fishing boat travel from a harbour on a bearing of 140 degree for 60 kilometer to an lsland a. How far due east does it travel b. Find the bearing required to return to the harbour .
60 cos(90-140)° = 60 cos50° = 38.56 km
Actually, the bearing of the island from the harbour is 140°
The heading of the ship was thus set to 140°
nice copy and paste there, yeet.
Now, why don't you answer part (b) ?
a. d = 60km[140o] CW from +y-axis.
X = 60*sin140 = 38.6 km.
b. 140o CW = 40o E. of S.
Return heading = 40o W. of N. = 320o CW.
So the heading is 180o greater .
To answer both parts of the question, we need to break down the movements of the boat.
a. How far does the boat travel due east?
First, let's draw a diagram to visualize the boat's movement:
```
Harbour (H) ---60 km---> Island (A)
```
The boat initially travels on a bearing of 140 degrees. To find how far the boat travels due east, we can break down the boat's movement into its north-south and east-west components using trigonometry.
We know that the bearing of 140 degrees makes an angle of 50 degrees with the north direction (90 degrees - 140 degrees = -50 degrees on a compass).
The east-west component can be found using the sine function, which relates the angle to the opposite side (east in this case) and the hypotenuse (total distance traveled). Let's calculate it:
sine(50 degrees) = east component / 60 km
Rearranging the equation, we get:
east component = sine(50 degrees) * 60 km
Using a calculator, we find:
east component ≈ 45.73 km
Therefore, the boat travels approximately 45.73 kilometers due east.
b. Finding the bearing required to return to the harbour:
To find the bearing required to return to the harbour, we need to consider the angle the boat makes with the north direction after reaching the island.
Since the boat travels 140 degrees from the harbour, it will need to return in the opposite direction, resulting in a bearing of 320 degrees.
Therefore, the bearing required to return to the harbour is 320 degrees.