The question in your image asks for the x-component (horizontal component) of a vector that is described as being 48 cm "north of east."

Here's how to solve this:

1. "North of east" means that the vector is at some angle northward from the east direction. However, since no angle is given, it's important to assume a likely scenario. If we assume that "north of east" means at a 45° angle (a common assumption when an angle is not specified), we can calculate the x-component using trigonometry.

2. The formula to find the x-component of a vector at an angle is: $R_x = R \cdot \cos(\theta)$ where:

   • $R_x$ is the x-component of the vector,
   • $R = 48 \, \text{cm}$ is the magnitude of the vector,
   • $\theta = 45^\circ$ is the angle north of east.

3. Using $\cos(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.707$: $R_x = 48 \, \text{cm} \cdot 0.707 \approx 33.94 \, \text{cm}$

4. The closest whole number answer from the provided choices would be 34 cm, but this doesn't match the options.

Looking at your options, the closest one is 42 cm, which suggests there may be a slightly different assumed angle. For example, an angle of around 30° north of east would give an x-component closer to 42 cm.

Would you like a more detailed exploration of the angle assumptions, or do you have any other questions?

Here are 5 relative questions for further exploration:

1. What is the y-component of the same vector?
2. How would the x-component change if the angle were 60° north of east?
3. If the resultant vector were 60 cm instead of 48 cm, how would that affect the x-component?
4. Can you find the total displacement if you are given both x and y components?
5. How do you decompose vectors into components for any general angle?

Tip: Always check for hidden assumptions like angles when directions like "north of east" are given without a specific degree.