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What is the direction of the displacement of this player? Give the angle counterclockwise relative to the right.

To determine the direction of the displacement of the player and find the angle counterclockwise relative to the right, I'll analyze the image provided.

The image depicts a baseball field where the player moves from the first base to the third base via second base. This movement forms a right-angled triangle, where the right angle is at second base.

1. **Determine the Points**: 
   - First Base (Point A)
   - Second Base (Point B)
   - Third Base (Point C)

2. **Displacement Vector**: 
   - The displacement vector points directly from Point A (first base) to Point C (third base).

3. **Angle Calculation**:
   - The angle we need to calculate is the angle between the horizontal line (from Point A to Point B, representing the "right" direction) and the displacement vector \(\vec{AC}\).

Since this is a standard problem involving the coordinates of a right-angled triangle:

- Assume the distance between each base is \(d\).
- The horizontal leg \(AB\) is along the x-axis (right direction), and \(BC\) is the vertical leg.

The angle \(\theta\) that the displacement vector makes with the horizontal axis can be found using the arctan function:

\[
\theta = \tan^{-1}\left(\frac{\text{Vertical displacement (BC)}}{\text{Horizontal displacement (AB)}}\right)
\]

Given that both legs \(AB\) and \(BC\) are equal (each base distance is \(d\)):

\[
\theta = \tan^{-1}\left(\frac{d}{d}\right) = \tan^{-1}(1) = 45^\circ
\]

**Answer**: The direction of the displacement of the player is **45 degrees counterclockwise** relative to the right.

Would you like further details, or do you have any other questions?

Here are some related questions you might consider:

1. How would the angle change if the distances between the bases were not equal?
2. What is the significance of the displacement vector in this scenario?
3. How do you calculate the magnitude of the displacement vector?
4. What would the angle be if the player moved from home plate to second base directly?
5. How can you calculate the total distance traveled by the player?

**Tip**: When working with angles and displacement vectors, always pay attention to the direction you define as "0 degrees" or "starting angle."

Learn how to determine the direction of a player's displacement on a baseball field, calculating the angle counterclockwise relative to the right. This problem involves using trigonometric concepts such as the arctangent function in a geometric context. Suitable for high school students.

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