A radar system is used to track a new experimental space launch vehicle. Early in the vehicle's flight trajectory, the azimuth angle ß is increasing with the constant rate dß/dt = 28°/s. The elevation angle y is increasing at the rate dy/dt= 40%s, and this rate is increasing at 5%s2. Know that the distance between O and Pis 2 m and that at this instant B = 0° and y = 30°. P dß/dt
A radar system is used to track a new experimental space launch vehicle. Early in the vehicle's flight trajectory, the azimuth angle ß is increasing with the constant rate dß/dt = 28°/s. The elevation angle y is increasing at the rate dy/dt= 40%s, and this rate is increasing at 5%s2. Know that the distance between O and Pis 2 m and that at this instant B = 0° and y = 30°. P dß/dt
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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i is not equal to 0
![**Radar System Tracking Problem**
A radar system is used to track a new experimental space launch vehicle. Early in the vehicle's flight trajectory, the azimuth angle \( \beta \) is increasing at the constant rate \(\frac{d\beta}{dt} = 28^\circ/\text{s}\). The elevation angle \( \gamma \) is increasing at the rate \(\frac{d\gamma}{dt} = 40^\circ/\text{s}\), and this rate is increasing at \( 5^\circ/\text{s}^2\). The distance between point \( O \) and point \( P \) is known to be 2 m, with \( \beta = 0^\circ \) and \( \gamma = 30^\circ \) at this instant.
**Diagram Explanation**
The diagram shows a radar antenna (represented as a parabolic dish on a stand) tracking the launch vehicle. The radar is pivoting around the \( z \) axis, which represents the azimuth change \( \frac{d\beta}{dt} \), and around the \( x \) axis, showing the elevation change \( \frac{d\gamma}{dt} \). The point \( P \) is the location of the vehicle, and \( O \) is the base point of the radar.
**Objective**
Determine the angular acceleration of the system. The answer given is:
\[ \text{Angular acceleration of the system is } (0.8298 \, \mathbf{i} + 0.0873 \, \mathbf{k}) \, \text{rad/s}^2. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91a5b069-6586-499b-b2a9-1d1bc7a326ea%2F88023821-286a-420c-956b-ad73b881e7b5%2Ft61w0cj_processed.png&w=3840&q=75)
Transcribed Image Text:**Radar System Tracking Problem**
A radar system is used to track a new experimental space launch vehicle. Early in the vehicle's flight trajectory, the azimuth angle \( \beta \) is increasing at the constant rate \(\frac{d\beta}{dt} = 28^\circ/\text{s}\). The elevation angle \( \gamma \) is increasing at the rate \(\frac{d\gamma}{dt} = 40^\circ/\text{s}\), and this rate is increasing at \( 5^\circ/\text{s}^2\). The distance between point \( O \) and point \( P \) is known to be 2 m, with \( \beta = 0^\circ \) and \( \gamma = 30^\circ \) at this instant.
**Diagram Explanation**
The diagram shows a radar antenna (represented as a parabolic dish on a stand) tracking the launch vehicle. The radar is pivoting around the \( z \) axis, which represents the azimuth change \( \frac{d\beta}{dt} \), and around the \( x \) axis, showing the elevation change \( \frac{d\gamma}{dt} \). The point \( P \) is the location of the vehicle, and \( O \) is the base point of the radar.
**Objective**
Determine the angular acceleration of the system. The answer given is:
\[ \text{Angular acceleration of the system is } (0.8298 \, \mathbf{i} + 0.0873 \, \mathbf{k}) \, \text{rad/s}^2. \]
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