A fishing boat travels from a harbour on a bearing of 140 degree for 60 km to an island how far due east does it travel?
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°
d = 60km[140o] Cw from +y-axis.
X = 60*sin140 = 38.56 km.
To find how far due east the fishing boat travels, we need to determine the component of its displacement in the east direction.
The bearing of 140 degrees means that the boat is traveling 140 degrees clockwise from the north direction. In other words, it is traveling towards the southeast.
Now, we can use basic trigonometry to find the eastward component of its displacement.
First, we can split the 140-degree bearing into two components: one towards the east and the other towards the south.
The southward component can be found using the sine function:
Sin(140) = Southward displacement / 60 km
Now, we can find the eastward component using the cosine function:
Cos(140) = Eastward displacement / 60 km
Since we want to find the eastward displacement, we rearrange the equation:
Eastward displacement = Cos(140) * 60 km
Calculating this value, we find:
Eastward displacement ≈ -31.24 km
The negative sign indicates that the boat is traveling in the west direction instead of the east direction. Therefore, the fishing boat travels a distance of approximately 31.24 km west.