3/65 The rocket moves in a vertical plane and is being propelled by a thrust T of 32 kN. It is also subjected to an atmospheric resistance R of 9.6 kN. If the rocket has a velocity of 3 km/s and if the gravitational acceleration is 6 m/s² at the altitude of the rocket, calculate the radius of curvature p of its path for the position described and the time-rate-of-change of the magnitude v of the velocity of the rocket. The mass of the rocket at the instant considered is 2000 kg.
3/65 The rocket moves in a vertical plane and is being propelled by a thrust T of 32 kN. It is also subjected to an atmospheric resistance R of 9.6 kN. If the rocket has a velocity of 3 km/s and if the gravitational acceleration is 6 m/s² at the altitude of the rocket, calculate the radius of curvature p of its path for the position described and the time-rate-of-change of the magnitude v of the velocity of the rocket. The mass of the rocket at the instant considered is 2000 kg.
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
Related questions
Question
Please solve for:
-Magnitude of acceleration of the rocket in m/s^2
-Direction of acceleration of the rocket relative to the ground in degrees
Box these answers, the unknowns that are asked for in the problem statement aren't necessary.
v = 6 m/s^2
p = 3000 km

Transcribed Image Text:**Problem 3/65: Rocket Motion in a Vertical Plane**
A rocket moves in a vertical plane and is propelled by a thrust \(T\) of 32 kN. It is also subjected to an atmospheric resistance \(R\) of 9.6 kN. The rocket has a velocity of 3 km/s. Given that the gravitational acceleration is 6 m/s\(^2\) at the altitude of the rocket, calculate the following:
1. The radius of curvature \(\rho\) of its path for the described position.
2. The time-rate-of-change of the magnitude \(v\) of the velocity of the rocket.
At the instant considered, the mass of the rocket is 2000 kg.
### Given Data:
- Thrust, \(T = 32\) kN
- Atmospheric resistance, \(R = 9.6\) kN
- Velocity, \(v = 3\) km/s = 3000 m/s
- Gravitational acceleration, \(g = 6\) m/s\(^2\)
- Mass of the rocket, \(m = 2000\) kg
### Calculation:
1. **Radius of Curvature (\(\rho\)):**
The radius of curvature \(\rho\) is dependent on the centripetal force acting on the rocket. The necessary centripetal force can be derived from the gravitational and thrust forces minus the drag force.
2. **Time-Rate-of-Change of Velocity (\(\dot{v}\)):**
The time-rate-of-change of the magnitude of velocity of the rocket can be determined using Newton's second law, applying the net force along the direction of the velocity vector.
The details of these computations would typically involve resolving the forces in the vertical direction and applying principles of dynamics to solve for the respective quantities. Piecing together the forces (thrust, drag, and gravity) and solving for the unknowns using the appropriate dynamical equations will yield the radius of curvature and the rate-of-change of velocity.
This problem illustrates the application of dynamics in an aerospace context, combining forces due to propulsion, resistance, and gravity to determine the motion characteristics of a rocket.

Transcribed Image Text:**Problem 3/65**
This image depicts a rocket that is inclined at an angle of 30° from the vertical axis. The rocket's orientation is illustrated with the body slightly tilted to the left. Two vectors, denoted as \( R \) (at the top of the rocket) and \( T \) (at the bottom of the rocket near the thrusters), are shown extending outward. Both vectors are depicted with red arrows, indicating the directions they represent.
- **Angle Measurement**: The rocket's orientation is measured at 30° from the vertical axis.
- **Vector \( R \)**: Located at the top of the rocket, pointing outward from the body.
- **Vector \( T \)**: Located at the bottom of the rocket near the thrusters, pointing outward in the opposite direction.
The purpose of this problem likely involves analyzing the forces and moments acting on the rocket. Understanding these vectors' directions in the diagram will be critical for solving the related physics or engineering problem.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education

Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education

Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY

Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning

Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY