https://file.aiquickdraw.com/mathbot/file/17308868386603uk9dtkc.jpg

To resolve a vector pointing northwest into its northerly and westerly components, we recognize that a northwest direction implies a 45-degree angle from both the north and west axes. Given the magnitude of the vector \( w = 50 \), we can break it down as follows:

1. **Northerly Component**:
   \[
   \text{Northerly component} = 50 \times \cos(45^\circ)
   \]

2. **Westerly Component**:
   \[
   \text{Westerly component} = 50 \times \sin(45^\circ)
   \]

Since \(\cos(45^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.7071\), we calculate each component:

\[
\text{Northerly component} = 50 \times 0.7071 \approx 35.36
\]
\[
\text{Westerly component} = 50 \times 0.7071 \approx 35.36
\]

### Answer:
- The northerly component has a magnitude of approximately **35.36**.
- The westerly component has a magnitude of approximately **35.36**.

Would you like further details or explanations on this? Here are some additional questions related to vector components:

1. How would the components change if the angle were different, say 30 degrees northwest?
2. What if the magnitude of the vector was different, like 60 instead of 50?
3. How do we calculate the components for a vector pointing southwest?
4. Can this method be used for any angle, or only for specific ones like 45 degrees?
5. How would these components be used in physics problems, like calculating displacement?

**Tip:** Remember that vectors pointing diagonally (like northwest or northeast) can be resolved into perpendicular components using trigonometric functions based on the angle.

A vector w of magnitude 50 points northwest. Resolve the vector into northerly and westerly components.

Learn how to resolve a vector of magnitude 50 pointing northwest into northerly and westerly components. This problem utilizes trigonometric functions to find each component, making it suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation