MTH022, 2024 Spring Assignment: Essay

发布时间：2024-05-13

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MTH022, 2024 Spring, FW

Assignment: Essay

# Instructions

(1). You (the student) are required to solve ONE of the two projects of mathematical modelling on the following pages and write up your work into a report.

(2). You are advised to restate the question, make appropriate assumptions, develop proper mathematical models with persuasive reasoning, calculate or compute, with programming code, the solutions, analyse or interpret the results, draw conclusions, and outline possible future work.

(3). You could make use of any knowledge you learnt in or out of the class. Make sure to include references you have consulted and cite content properly in the context.

(4). You should write in a professional way with appropriate usage of various settings of format, such as sections, subsections, paragraphs, table of contents, references, appendices (computer programming code or else), figures, tables, lists, etc. Your report should include one page of summary and be of at least 5 pages of A4 paper with proper font, line spacing, margins, etc., but not exceed 25 pages.

(5). You may goto LM Core Archive 2022-23 / Mathematical Modelling page (see the link below; the self-enrolment key is mm@XJTLU2006 if you were the first time to access it) to find award-winning papers of MCM/ICM for your reference of writing structure, style, etc.

https://core-archive22-23.xjtlu.edu.cn/course/view.php?id=5685

(6). You could prepare your report with any software, such as MS Word, LaTeX, or the like. But be sure to finish everything in a single PDF document. An MCM/ICM LaTeX template is provided for your reference on the module page of MTH022 of LM Core.

(7). You are required to submit the PDF report to the provided link ‘Assignment Essay Submission’ on the module page of MTH022 of LM Core, by the due time 17:00, Thursday, 06 June 2024. Please do not submit any other supportive files.

(8). The mark of this essay assignment will contribute 30% to your overall assessment of the module MTH022.

Project 1

As the time for final exams approaches in school, the exam often becomes a hot topic of discussion among students. With the spread of information, various rumors about the exam may arise, such as rumors that a certain subject will feature specific question types, or that the exam difficulty will be easier than previous years. These rumors may spread rapidly among students through word of mouth, and social media platforms such as Zhitiao, or Wechat Moments. The spread of rumors may potentially impact the study mentality and learning plans of the students, leading to inaccurate information, increased anxiety, and even affecting their normal study habits and motivation.

1. Please establish a mathematical model to describe the spread of final exam rumors among students at XJTLU.

2. Someone created a rumor about the cancellation of the final exams at 8 am, and by noon, 200 students had already heard about it. How long will it take for this rumor to spread throughout the university?

Project 2

Drones have become increasingly prevalent on the modern battlefield due to their abil-ity to autonomously track and engage enemies. An autonomous military drone uses a predetermined strategy to chase an enemy.

Chasing a Stationary Target

Suppose a drone is strategically positioned a miles to the east of a stationary target. The drone maintains a constant speed of b miles per hour, while a strong wind blows from the south at a speed of w miles per hour.

(1) Create a mathematical model to determine the flight path of the drone as it navigates towards the target.

(2) Calculate the wind speed at which the drone would lose its capability to reach the target, exceeding a critical threshold rendering it powerless.

(3) Calculate the wind speed at which the drone successfully reaches its target, achieving a synchronized interception.

Pursuing a Moving Target

On a windless day, a target is in motion, progressing northward at a consistent speed of 8 yards per second. Initially, the drone is strategically placed directly opposite the target’s position. Upon detecting the target, the drone immediately accelerates to a speed of 10 yards per second. At this point, the target has only 60 yards remaining to reach a stronghold.

Determine whether it is tactically advantageous to send the drone under these con- ditions to intercept and halt the advancing target from reaching the stronghold.