Substitute this expression for m and the values of e, A, Cp and k into the differential equation above to show that dv 18, 000 – 0. 15v² dt 3000 – 6t
Substitute this expression for m and the values of e, A, Cp and k into the differential equation above to show that dv 18, 000 – 0. 15v² dt 3000 – 6t
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
Related questions
Question
First solve numerically using eulers method
![Accounting for viscous drag and fuel-burning, the one-dimensional equation of motion for a rocket-
propelled vehicle travelling along a horizontal surface is
dv
1
dm
m
dt
= -PACDU -k
dt
where (in SI units) p = 1.2 is the density of air, A = 1 is the effective frontal area of the vehicle,
= 3000 is the rocket's thrust coefficient. Furthermore, if the
CD = 0. 25 is the drag coefficient and k
mass of the vehicle after fuelling is 3000 kg and the fuel burn rate is a linear 6 kg s, then one may
%3D
S
write
m =
3000 – 6t
Substitute this expression for m and the values of p, A, Cp and k into the differential equation
above to show that
dv
18, 000 – 0. 15v
%3D
dt
3000 – 6t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea4cf128-49a1-49a2-8779-32e70345ec36%2F42a3eb66-f3fb-4291-ac9b-1e67bd666572%2Fe00i9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Accounting for viscous drag and fuel-burning, the one-dimensional equation of motion for a rocket-
propelled vehicle travelling along a horizontal surface is
dv
1
dm
m
dt
= -PACDU -k
dt
where (in SI units) p = 1.2 is the density of air, A = 1 is the effective frontal area of the vehicle,
= 3000 is the rocket's thrust coefficient. Furthermore, if the
CD = 0. 25 is the drag coefficient and k
mass of the vehicle after fuelling is 3000 kg and the fuel burn rate is a linear 6 kg s, then one may
%3D
S
write
m =
3000 – 6t
Substitute this expression for m and the values of p, A, Cp and k into the differential equation
above to show that
dv
18, 000 – 0. 15v
%3D
dt
3000 – 6t
![plot a fully labelled graph of your results for 0 < t < 200 s,
state the recursion relations (linking tn to tr-1 and Un to Un-1) you used to perform your
numerical solution; and,
state the maximum speed that the vehicle is able to reach in the interval 0 < t < 200 s.
(B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea4cf128-49a1-49a2-8779-32e70345ec36%2F42a3eb66-f3fb-4291-ac9b-1e67bd666572%2Fp3p2tb8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:plot a fully labelled graph of your results for 0 < t < 200 s,
state the recursion relations (linking tn to tr-1 and Un to Un-1) you used to perform your
numerical solution; and,
state the maximum speed that the vehicle is able to reach in the interval 0 < t < 200 s.
(B)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![Algebra and Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305071742/9781305071742_smallCoverImage.gif)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning