Final answer:
The y-component of the displacement when a ship is displaced 100 km at a bearing of W 60 degrees N, with east and north being positive, is calculated using the cosine of the angle, which results in a y-component of 50.0 km.
Step-by-step explanation:
If east is positive and north is positive, the y-component of the displacement when a ship is displaced 100 km at a bearing of W 60 degrees N needs to be calculated. Since the displacement is in the north-west direction, the northward (positive y-direction) component can be found by using the cosine function of the angle, because the angle given is with respect to the west direction. We must note that since the ship is moving northward, the y-component will still be positive.
To find the y-component, we can use the formula:
- y-component = displacement × cos(angle)
Substitute the given values into the formula:
y-component = 100 km × cos(60°)
This calculates to:
y-component = 100 km × 0.5
y-component = 50.0 km
Therefore, the correct answer is a) 50.0 km.