Refer to figure 1. Another cart has two vectors that help describe its overall motion. What is the overall direction and magnitude of the cart's motion (i.e. find the resultant vector in x, y notation). Then convert your answer into magnitude - angle format. 260.0° 200.0 m/s 100.0 m/s 60.0° Figure 1: Cart #2

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Chapter1: Units, Trigonometry. And Vectors
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### Vector Analysis of Cart Motion

**Problem Statement:**
1. Refer to figure 1. Another cart has two vectors that help describe its overall motion. What is the overall direction and magnitude of the cart's motion (i.e., find the resultant vector in \( \hat{x}, \hat{y} \) notation). Then convert your answer into magnitude-angle format.

**Figure Explanation:**

- **Vector 1**: 
  - Magnitude: 100.0 m/s
  - Angle: 60.0° from the positive x-axis
  - This vector points upward to the right.

- **Vector 2**:
  - Magnitude: 200.0 m/s
  - Angle: 260.0° from the positive x-axis
  - This vector points downward to the left.

These vectors represent the motion components of Cart #2. The figure illustrates both vectors starting from a common point, indicating that they are to be added vectorially to find the resultant vector of the cart's motion. 

To find the overall direction and magnitude:
1. Resolve each vector into its x and y components.
2. Sum the corresponding components to obtain the resultant vector.
3. Convert the resultant from component form \( \hat{x}, \hat{y} \) to magnitude-angle form.
Transcribed Image Text:### Vector Analysis of Cart Motion **Problem Statement:** 1. Refer to figure 1. Another cart has two vectors that help describe its overall motion. What is the overall direction and magnitude of the cart's motion (i.e., find the resultant vector in \( \hat{x}, \hat{y} \) notation). Then convert your answer into magnitude-angle format. **Figure Explanation:** - **Vector 1**: - Magnitude: 100.0 m/s - Angle: 60.0° from the positive x-axis - This vector points upward to the right. - **Vector 2**: - Magnitude: 200.0 m/s - Angle: 260.0° from the positive x-axis - This vector points downward to the left. These vectors represent the motion components of Cart #2. The figure illustrates both vectors starting from a common point, indicating that they are to be added vectorially to find the resultant vector of the cart's motion. To find the overall direction and magnitude: 1. Resolve each vector into its x and y components. 2. Sum the corresponding components to obtain the resultant vector. 3. Convert the resultant from component form \( \hat{x}, \hat{y} \) to magnitude-angle form.
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