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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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)
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)
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