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MATH36031 Project

创建日期：2024-05-15 15:12:21

所属分类：数学mathematics

标签： MATH36031

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MATH36031 Project

In this project, you will investigate the problem of a fox chasing a rabbit by solving differential
equations modelling their positions at different times. The initial configuration is shown in
Figure 1, where the fox starts chasing the rabbit while the rabbit tries to escape from its
predator and moves towards its burrow instantaneously. The fox is initially located1 at
(−250,−550), pursues the rabbit with the initial speed sf0 = 16m/s in one of the following
two possible ways:
Warehouse
F(-250,-550)
S(-200,-400)
R(0,0)
B(-600,600)
N(-200,0)
Figure 1: Coordinates (in metres) of the fox (F), the rabbit (R) and its burrow (B) and the
two corners (S,N) of the warehouse.
if the rabbit is in sight, the fox’s attack path points directly towards the rabbit (the
direction of the velocity vector of the fox is exact from the fox to the rabbit);
if the view of the rabbit is blocked by the corner S of an impenetrable warehouse
(assuming that the warehouse is extended indefinitely to the west), then the fox runs
directly towards this corner. If the rabbit is still not in sight when the corner is
reached, then the fox moves parallel to the N-S perimeter of the warehouse until it sees
the rabbit.
1The subscripts f and r denote the fox and rabbit respectively. The units of the coordinates are metres.
1
The rabbit, initially located at the origin (0, 0), runs towards its burrow at (−600, 600)
in a straight line with initial speed sr0 = 13m/s.
Question 1: Constant speeds.. Assuming that both the fox and the rabbit run with
constant speeds sf0 = 16m/s and sr0 = 13m/s respectively, determine whether the rabbit
can be captured before it reaches its burrow. The rabbit is considered to be captured by the
fox, if the distance between them is smaller than or equal to 0.1 meter.
Question 2: Diminishing speeds. Let us consider a more realistic scenario, when
the hungry fox meets the tired rabbit. Because neither the fox nor the rabbit are in their
best conditions, their chasing/escaping speeds diminish in time, according to the amount of
distance (starting from the time they find each other and start running) they have travelled
so far. More precisely, their speeds at time t are given by
sf (t) = sf0e
−µfdf (t), sr(t) = sr0e−µrdr(t),
where sf0 = 16m/s and sr0 = 13m/s are the same initial speeds as above, µf = 0.0002m
−1
and µr = 0.0008m
−1 are the rates of the diminishing speeds, df (t) and dr(t) are the distance
they have travelled up to time t(> 0). Determine whether the rabbit can be captured before
it reaches its burrow. (You may assume that this diminishing speed starts from t = 0).
Outputs required You are required to submit a report (maximum 8 pages including
any appendices) in pdf form via the Turnitin submission box on Blackboard. Additionally
you need to submit your m-files used for the MATLAB codes via the Blackboard submission
box. In your report give (i) the time T and the location of the fox when either the rabbit is
captured or the rabbit escapes to the burrow; (ii) the distance travelled by the fox in time
T . Additionally provide a plot showing the paths taken by both animals.
Additional information and guidelines
1. All coding must be done in MATLAB.
2. Treat both the fox and the rabbit as points, without worrying about their finite sizes
(as in most models).
3. The questions can be answered with different approaches, but the preferred way is to
use the built-in ODE solver ode45 discussed during the lectures.
4. Avoid using hard-coded numbers. Any number in your code should either be given as
initial condition, or be derived from these conditions.
5. Keep your page length not exceeding eight A4 pages, with a font size no smaller
than 11, and page margins no smaller than 2cm. There is no need for a title page for
a relative short report like this. If more than 8 pages are submitted only the
first 8 pages will be marked and the rest of the submission will be ignored.
6. List the complete code of the whole function at the end of each question, or in an
appendix. Make your source code more readable, by keeping the indentation and
2
stylistic features, and can be copied from your submitted. Your published results
should be reproducable from the code attached.
7. Have a look at the generic rubric about how your report will be marked, and also the
intended learning outcomes about what you are expected to achieve in the end.
8. Avoid copying (too many) sentences directly from the project description, and try to
restate the problem with your own words or examples if possible.
9. You may use your report in the future as evidences of written work, so take it seriously.
10. Your target audience is a fellow student on your course: explain the questions so that
the report can be understood without this project description and your approach can
be implemented in another computer. The report should indicate to the reader how
well you understand the problem and the approach you have taken, the validation and
other checks that you made to ensure your results are credible. Reports submitted
containing codes only and with no explanations of how the problem was solved, will
result in a failing mark, even though the codes may work perfectly well and give the
correct answers.
11. Balance the explanation of the approach and the comments in the code. Avoid under-
commenting and over-commenting.
12. Aim for precision and clarity of writing.
13. Since there is no final exam, you are advised to spend at least 15 hours on each project,
with additional self-study if you are less experience with computer programming. Re-
member for a 10 credit module like this one, you are expect to spend 100 = 10 Ö 10
hours in total (including lectures, labs, self-study and coursework).
14. Please do not put any personal information on the report, only your student ID number.
15. The submission box (via Blackboard and Turnitin) for each project will be open two
weeks before the deadline, and you are encouraged to submit an early draft to see
how Turnitin works on Blackboard. Only your last submission will be marked, and
DO NOT submit anything after the deadline. Any late penalty will be applied by
the Teaching and Learning Support Office according to the Undergraduate Student
Handbook, and any extension has to be approved from the Office too (not from the
lecturer).
16. This coursework is meant to be an individual piece of work and the reports must
be written by yourself. Your attention is drawn to the section 4.10 on Academic
Malpractice on page 36 of the undergraduate handbook. Cases of plagairism will
be treated seriously and individuals will be reported to the University Disciplinary
Committee.

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 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