Final answer:
The pilot is 8660 km further North and 5000 km further West than when she started.
Step-by-step explanation:
To find how much further North the pilot is than when she started, we need to determine the North component of the displacement. When moving in the direction [N30.0° W], the North component can be found using trigonometry. We can use the cosine function to find the North component:
North component = (total displacement) * cos(angle)
Substituting the values:
North component = (1.00 x 10^4 km) * cos(30.0°)
Calculating the North component gives us:
North component = 1.00 x 10^4 km * 0.866 = 8660 km
Therefore, the pilot is 8660 km further North than when she started.
To find how much farther West the pilot is than when she started, we need to determine the West component of the displacement. Using trigonometry, we can use the sine function to find the West component:
West component = (total displacement) * sin(angle)
Substituting the values:
West component = (1.00 x 10^4 km) * sin(30.0°)
Calculating the West component gives us:
West component = 1.00 x 10^4 km * 0.5 = 5000 km
Therefore, the pilot is 5000 km further West than when she started.