https://file.aiquickdraw.com/mathbot/file/1726655434553c981pv8u.jpg

The image shows two vector problems. Let's break them down:

### (b) Velocity vector decomposition:
- **Given**: 
  - A velocity \( v = 75 \, \text{km/h} \) at an angle of \( 50^\circ \) north of west.
  
- **Task**: 
  - Find the horizontal and vertical components of the velocity (\( v_x \) and \( v_y \)).

- **Solution**:
  - \( v_x = v \cos(50^\circ) \)
  - \( v_y = v \sin(50^\circ) \)
  
  Since the vector is directed north of west:
  - \( v_x \) will be negative (since it's westward).
  - \( v_y \) will be positive (since it's northward).

### (c) Force vector decomposition:
- **Given**: 
  - A force \( F = 800 \, \text{N} \) at an angle of \( 70^\circ \) south of west.

- **Task**:
  - Find the horizontal and vertical components of the force (\( F_x \) and \( F_y \)).

- **Solution**:
  - \( F_x = F \cos(70^\circ) \)
  - \( F_y = F \sin(70^\circ) \)
  
  Since the force is directed south of west:
  - \( F_x \) will be negative (since it's westward).
  - \( F_y \) will also be negative (since it's southward).

Would you like detailed calculations for these components? 

Here are 5 related questions to explore:
1. What is the significance of breaking vectors into components in physics?
2. How does the angle's reference direction (e.g., north of west) affect the sign of components?
3. Can we find the magnitude of a vector given its components?
4. How does trigonometry help in vector analysis?
5. What are real-life applications of vector decomposition?

**Tip**: Always pay attention to the direction of angles to assign correct signs to vector components.

Two vector problems: (b) Velocity vector decomposition with a velocity of 75 km/h at an angle of 50° N of W, and (c) Force vector decomposition with a force of 800 N at an angle of 70° S of W.

Explore how to decompose a velocity of 75 km/h at 50° N of W and a force of 800 N at 70° S of W into their horizontal and vertical components using trigonometric functions. This solution includes step-by-step vector analysis, perfect for Grades 11-12 or early physics courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation