Homework Help is Here – Start Your Trial Now!
Math
Calculus
Accounting for viscous drag and fuel-burning, the one-dimensional equation of motion for a rocket- propelled vehicle travelling along a horizontal surface is 1 PACv² – k- dt dv dm m dt where (in Sl units) p = 1.2 is the density of air, A = 1 is the effective frontal area of the vehicle, C, = 0.25 is the drag coefficient and k = 3000 is the rocket's thrust coefficient. Furthermore, if the mass of the vehicle after fuelling is 3000 kg and the fuel burn rate is a linear 6 kg s-1, then one may write m = 3000 – 6t Substitute this expression for m and the values of p, A, C, and k into the differential equation above to show that dv_ 18,000 – 0.15v dt 3000 – 6t and solve this numerically using Euler's method in MATLAB with the initial condition v(0) = 0 and the step size h = 5 (include a screenshot), plot a fully labelled graph of your results for 0 sts 200 s, state the recursion relations (linking t, to tn-1 and v, to vn-1) you used to perform your numerical solution; and, state the maximum speed that the vehicle is able to reach in the interval 0 st S 200 s.

Accounting for viscous drag and fuel-burning, the one-dimensional equation of motion for a rocket- propelled vehicle travelling along a horizontal surface is 1 PACv² – k- dt dv dm m dt where (in Sl units) p = 1.2 is the density of air, A = 1 is the effective frontal area of the vehicle, C, = 0.25 is the drag coefficient and k = 3000 is the rocket's thrust coefficient. Furthermore, if the mass of the vehicle after fuelling is 3000 kg and the fuel burn rate is a linear 6 kg s-1, then one may write m = 3000 – 6t Substitute this expression for m and the values of p, A, C, and k into the differential equation above to show that dv_ 18,000 – 0.15v dt 3000 – 6t and solve this numerically using Euler's method in MATLAB with the initial condition v(0) = 0 and the step size h = 5 (include a screenshot), plot a fully labelled graph of your results for 0 sts 200 s, state the recursion relations (linking t, to tn-1 and v, to vn-1) you used to perform your numerical solution; and, state the maximum speed that the vehicle is able to reach in the interval 0 st S 200 s.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Question 4 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 PAC,v² – k- dt where (in Sl units) p = 1.2 is the density of air, A = 1 is the effective frontal area of the vehicle, C, = 0.25 is the drag coefficient and k = 3000 is the rocket's thrust coefficient. Furthermore, if the mass of the vehicle after fuelling is 3000 kg and the fuel burn rate is a linear 6 kg s-, then one may write m = 3000 – 6t Substitute this expression for m and the values of p, A, C, and k into the differential equation above to show that dv 18,000 – 0.15v? 3000 – 6t dt and solve this numerically using Euler's method in MATLAB with the initial condition v(0) = 0 and the step size h = 5 (include a screenshot), • plot a fully labelled graph of your results for 0 <t< 200 s, state the recursion relations (linking tn to tn-1 and vn to vn-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)
Transcribed Image Text:Question 4 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 PAC,v² – k- dt where (in Sl units) p = 1.2 is the density of air, A = 1 is the effective frontal area of the vehicle, C, = 0.25 is the drag coefficient and k = 3000 is the rocket's thrust coefficient. Furthermore, if the mass of the vehicle after fuelling is 3000 kg and the fuel burn rate is a linear 6 kg s-, then one may write m = 3000 – 6t Substitute this expression for m and the values of p, A, C, and k into the differential equation above to show that dv 18,000 – 0.15v? 3000 – 6t dt and solve this numerically using Euler's method in MATLAB with the initial condition v(0) = 0 and the step size h = 5 (include a screenshot), • plot a fully labelled graph of your results for 0 <t< 200 s, state the recursion relations (linking tn to tn-1 and vn to vn-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
steps

Step by step

Solved in 4 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS