### Problem Statement:A helicopter starts from rest at point A and travels along the straight-line path with a constant acceleration \( a \). If the speed \( v \) = 23 m/s when the altitude of the helicopter is \( h \) = 37 m, determine the values of \(\dot{r}\), \(\ddot{r}\), \(\dot{\theta}\), and \(\ddot{\theta}\) as measured by the tracking device at O. At this instant, \(\theta\) = 35°, and the distance \( d \) = 177 m. Neglect the small height of the tracking device above the ground.### Diagram Description:The diagram illustrates a helicopter following a linear path from point A up to a point above the ground, with the tracking device at point O. - **Points Noted:** - \( O \): Point where the tracking device is located. - \( A \): Starting point of the helicopter. - \( h \): Altitude of the helicopter from the ground, shown as a vertical line. - \( d \): Horizontal distance from point A to directly below the helicopter's current position. - \( r \): Distance from point O to the helicopter’s current location. - Line segment \( v \): Indicates the velocity vector of the helicopter. - \(\theta\): Angle between \( r \) and the horizontal ground. ### Diagram Components:- **Tracking device \( O \)** at the origin, measuring positions, angles, and distances.- **Helicopter Path**, denoted by a dashed orange line, beginning at point \( A \) and moving upwards.- **Angle \( \theta \)**, the angle formed between \( r \) and the horizontal axis.### Task:Determine the following values:- \(\dot{r}\) (Rate of change of \( r \))- \(\ddot{r}\) (Acceleration along \( r \))- \(\dot{\theta}\) (Rate of change of angle \( \theta \))- \(\ddot{\theta}\) (Angular acceleration)### Answers:- \(\dot{r} =\) [_______] m/s- \(\ddot{r} =\) [_______] m/s²- \(\dot{\theta} =\) [_______] rad/s- \(\ddot{\

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A helicopter starts from rest at point A and travels along the straight-line path with a constant acceleration a. If the speed v = 23 m/s when the altitude of the helicopter is h = 37 m, determine the values of r, r, 0, and 0 as measured by the tracking device at O. At this instant, 0 = 35°, and the distance d = 177 m. Neglect the small height of the tracking device above the ground. r Th Answers: i m/s m/s² i rad/s i rad/s² a D: =

A helicopter starts from rest at point A and travels along the straight-line path with a constant acceleration a. If the speed v = 23 m/s when the altitude of the helicopter is h = 37 m, determine the values of r, r, 0, and 0 as measured by the tracking device at O. At this instant, 0 = 35°, and the distance d = 177 m. Neglect the small height of the tracking device above the ground. r Th Answers: i m/s m/s² i rad/s i rad/s² a D: =

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:

A helicopter starts from rest at point A and travels along the straight-line path with a constant acceleration \( a \). If the speed \( v \) = 23 m/s when the altitude of the helicopter is \( h \) = 37 m, determine the values of \(\dot{r}\), \(\ddot{r}\), \(\dot{\theta}\), and \(\ddot{\theta}\) as measured by the tracking device at O. At this instant, \(\theta\) = 35°, and the distance \( d \) = 177 m. Neglect the small height of the tracking device above the ground.

### Diagram Description:

The diagram illustrates a helicopter following a linear path from point A up to a point above the ground, with the tracking device at point O.

- **Points Noted:**
- \( O \): Point where the tracking device is located.
- \( A \): Starting point of the helicopter.
- \( h \): Altitude of the helicopter from the ground, shown as a vertical line.
- \( d \): Horizontal distance from point A to directly below the helicopter's current position.
- \( r \): Distance from point O to the helicopter’s current location.
- Line segment \( v \): Indicates the velocity vector of the helicopter.
- \(\theta\): Angle between \( r \) and the horizontal ground.

### Diagram Components:

- **Tracking device \( O \)** at the origin, measuring positions, angles, and distances.
- **Helicopter Path**, denoted by a dashed orange line, beginning at point \( A \) and moving upwards.
- **Angle \( \theta \)**, the angle formed between \( r \) and the horizontal axis.

### Task:

Determine the following values:
- \(\dot{r}\) (Rate of change of \( r \))
- \(\ddot{r}\) (Acceleration along \( r \))
- \(\dot{\theta}\) (Rate of change of angle \( \theta \))
- \(\ddot{\theta}\) (Angular acceleration)

### Answers:

- \(\dot{r} =\) [_______] m/s
- \(\ddot{r} =\) [_______] m/s²
- \(\dot{\theta} =\) [_______] rad/s
- \(\ddot{\

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