**Title**: Converting Polar Coordinates to Component Form**Instructions**: Learn how to express position vectors in component form given their polar coordinates.---**Problem Statement**: Obtain expressions in component form for the position vectors with the following polar coordinates.(a) **13.0 m, 140°** counterclockwise from the +x axis- **Component Form**: \(\vec{R} = 8.36 \, \text{m}\) (Note: The answer box indicates it's incorrect with a red "x".)(b) **3.80 cm, 80.0°** counterclockwise from the +x axis- **Component Form**: \(\vec{R} = 3.74 \, \text{cm}\) (Note: The answer box indicates it's incorrect with a red "x".)---**Explanation of Components**:When converting polar coordinates \((r, \theta)\) to rectangular (cartesian) coordinates \((x, y)\), use the formulas:- \( x = r \cdot \cos(\theta) \)- \( y = r \cdot \sin(\theta) \)The problem requires calculating these values to obtain the vector \(\vec{R}\) in terms of \(x\) and \(y\) components.**Note**: It seems there is an error in calculation as indicated by the incorrect marks next to the inputs. Ensure calculations adhere to the formula and verify trigonometric function entries.---**Graph/Diagram Explanation**: This image does not contain any graphs or diagrams.**Tips for Success**:1. **Check Units**: Always ensure unit consistency (meters vs. centimeters).2. **Trigonometry Review**: Familiarize yourself with sine and cosine functions to accurately convert angles.3. **Double-Check**: Revisiting calculations can help correct common errors.

(given) Polar coordinate of a point is (13.0, 1400) x component of the point in cartesian coordinate…

Obtain expressions in component form for the position vectors having the following polar coordinates. (a) 13.0 m, 140° counterclockwise from the +x axis R = 8.36 m (b) 3.80 cm, 80.0° counterclockwise from the +x axis R = 3.74 cm

Obtain expressions in component form for the position vectors having the following polar coordinates. (a) 13.0 m, 140° counterclockwise from the +x axis R = 8.36 m (b) 3.80 cm, 80.0° counterclockwise from the +x axis R = 3.74 cm

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

**Title**: Converting Polar Coordinates to Component Form

**Instructions**: Learn how to express position vectors in component form given their polar coordinates.

---

**Problem Statement**: Obtain expressions in component form for the position vectors with the following polar coordinates.

(a) **13.0 m, 140°** counterclockwise from the +x axis

- **Component Form**: \(\vec{R} = 8.36 \, \text{m}\) (Note: The answer box indicates it's incorrect with a red "x".)

(b) **3.80 cm, 80.0°** counterclockwise from the +x axis

- **Component Form**: \(\vec{R} = 3.74 \, \text{cm}\) (Note: The answer box indicates it's incorrect with a red "x".)

---

**Explanation of Components**:

When converting polar coordinates \((r, \theta)\) to rectangular (cartesian) coordinates \((x, y)\), use the formulas:

- \( x = r \cdot \cos(\theta) \)
- \( y = r \cdot \sin(\theta) \)

The problem requires calculating these values to obtain the vector \(\vec{R}\) in terms of \(x\) and \(y\) components.

**Note**: It seems there is an error in calculation as indicated by the incorrect marks next to the inputs. Ensure calculations adhere to the formula and verify trigonometric function entries.

---

**Graph/Diagram Explanation**: This image does not contain any graphs or diagrams.

**Tips for Success**:

1. **Check Units**: Always ensure unit consistency (meters vs. centimeters).
2. **Trigonometry Review**: Familiarize yourself with sine and cosine functions to accurately convert angles.
3. **Double-Check**: Revisiting calculations can help correct common errors.

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