### Problem StatementThe particle \( P \) moves along the parabolic surface shown. When \( x = 0.18 \) m, the particle speed is \( v = 3.4 \) m/s. For this instant, determine the corresponding values of \( r \), \( \dot{r} \), \( \theta \), and \( \dot{\theta} \). Both \( x \) and \( y \) are in meters.### Diagram ExplanationIn the provided diagram:- The particle \( P \) is moving along a parabolic path defined by the equation \( y = 7x^2 \).- The diagram is plotted on an x-y coordinate system where the parabolic path opens upwards.- The radius vector \( r \) extends from the origin \( O \) to the particle \( P \).- The angle \( \theta \) is measured counterclockwise from the x-axis to the radius vector \( r \).### AnswersPlease fill in the values:- \( r = \) \_\_\_\_\_ m- \( \dot{r} = \) \_\_\_\_\_ m/s- \( \theta = \) \_\_\_\_\_ °- \( \dot{\theta} = \) \_\_\_\_\_ rad/s

To find : The r,r˙,θ and θ˙. Free body diagram : The free body diagram is, Formula used : Use the…

The particle P moves along the parabolic surface shown. When x = 0.18 m, the particle speed is v= 3.4 m/s. For this instant determine the corresponding values of r, r, 0, and 0. Both x and y are in meters. I 8 y = 7x² P

The particle P moves along the parabolic surface shown. When x = 0.18 m, the particle speed is v= 3.4 m/s. For this instant determine the corresponding values of r, r, 0, and 0. Both x and y are in meters. I 8 y = 7x² P

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Statement

The particle \( P \) moves along the parabolic surface shown. When \( x = 0.18 \) m, the particle speed is \( v = 3.4 \) m/s. For this instant, determine the corresponding values of \( r \), \( \dot{r} \), \( \theta \), and \( \dot{\theta} \). Both \( x \) and \( y \) are in meters.

### Diagram Explanation

In the provided diagram:
- The particle \( P \) is moving along a parabolic path defined by the equation \( y = 7x^2 \).
- The diagram is plotted on an x-y coordinate system where the parabolic path opens upwards.
- The radius vector \( r \) extends from the origin \( O \) to the particle \( P \).
- The angle \( \theta \) is measured counterclockwise from the x-axis to the radius vector \( r \).

### Answers

Please fill in the values:
- \( r = \) \_\_\_\_\_ m
- \( \dot{r} = \) \_\_\_\_\_ m/s
- \( \theta = \) \_\_\_\_\_ °
- \( \dot{\theta} = \) \_\_\_\_\_ rad/s

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