The displacement of 10 km at an angle of 30 degrees north of west has a northward component of 5 km. Here option A is correct.
When describing a displacement of 10 km in a direction of 30 degrees north of west, it implies a vector quantity that combines both distance and direction. To find the northward component of this displacement, we can use trigonometric functions.
Consider a right-angled triangle formed by the displacement vector, where the 30-degree angle is between the vector and the westward direction. The northward component is the side opposite the 30-degree angle. Using the sine function, we can determine this component:
The northward component = Displacement × sin(Angle)
The northward component = 10 km × sin(30 degrees)
The northward component = 10 km × (1/2)
The northward component = 5 km
Therefore, the correct answer is a) 10 km north, as the displacement has a northward component of 5 km.