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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
First solve numerically using eulers method

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

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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