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DESIGNING A ROLLER COASTER
创建日期：2024-09-04 15:26:02
所属分类：数学mathematics
标签： Mathematical
DESIGNING A ROLLER COASTER

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DESIGNING A ROLLER COASTER


This activity explores the interaction of functions in developing a roller coaster.

Design Brief

The task for the investigation is to design a track for a roller coaster.

Part 1

A roller coaster requires that a series of functions be fitted together, with a starting and finishing gradient for each section that matches that of another function.

One section of the track is to be given as a parabola that meets the following conditions:

•    it has an initial slope on the ascent as 0.7

•    it has a final slope on the descent as -1.8

•    the origin is located at the beginning of the initial slope.

•    the horizontal distance between the final and initial slope is 16 m.

Find a parabola that meets this requirement.

For the track to be smooth there can’t be abrupt changes in direction. There will be two linear segments at either end of the parabola, L1  and L2, such that there is a smooth transition at the transition points P and Q. Therefore, you want the linear segments to be tangents at these points.


Find the equations of the linear segments.

Part 2

Complete a design for a roller coaster using appropriate functions (which may include, but is not limited to, Polynomials, Exponentials and Trigonometric). You will need to pay particular attention to ensure that the trolley is able to run smoothly over the track. You are required to include the functions that you found in Part 1, although you may translate it to a different position if you wish (show evidence).

Some additional factors that you may like to consider:

•    The practicality of your Roller Coaster (including length and height constraints)

•    It may be worth looking at information about roller coasters, and then using that as a reference to consider strengths, limitations, etc

•    using software like Geogebra or similar to draw a diagram of your track

At the conclusion, you are to submit the following:

•    A diagram of your track, showing each function with its domain.

•    Evidence that your track is smooth

•    A discussion as to the practicality of the track, considering any limitations that you needed to deal with.

Folio Tasks: Report Writing Guidelines

Specifications:

•    Each investigation report, excluding bibliography and appendices if used, must be a maximum of 15 A4, single sided pages, with minimum

font size 10. Page reduction, such as 2 A4 pages reduced to fit on 1 A4 page, is not acceptable.

•   Conclusions, interpretations and/or arguments that are required for the assessment must be presented in the report, and not in an appendix.

•   Appendices should only be used to support the report, and should not form part of the assessment decision.

Language Conventions

•   Written sections (Introduction & Conclusion) must include

o appropriate paragraphing

o full sentences with correct grammar and structure

•   Whenever possible the use of “I”, “me”, “we” should be avoided.

The Structure of a Mathematical Report

Introduction

This section describes what the investigation will be about. It should include:

•    any background (set the scene) information relevant to the main focus of the investigation

•    the aim/purpose of the investigation (including the definition of any key terms (mathematical and non-mathematical) relevant to the context of the problem)

•    a description of how the investigation will be carried out

Mathematical Investigations & Analysis

This section contains all the data/information/calculations/results gathered or produced in the course of the investigation. It includes:

•    complete solutions to all set tasks set out in a clear and logical way

•    appendices should only be used if there are extensive repetitive calculations and must be referenced appropriately

•    all results displayed appropriately and clearly (tables; graphs; diagrams)

•    clear communication of all relevant information (including correct mathematical notation)

•    interpretation and analysis of all results using complete sentences

•    where applicable reference should be made to the reasonableness of the results (in terms of the context of the problem being investigated) and any possible limitations of the interpreted results/original problem.

Conclusion

This section includes:

•    a summary of all the main findings

• a clear statement of the overall conclusion(s)/solution (relating directly back to the aim)

•    an evaluation of the results and methods used, including a comment on (where applicable)

o any assumptions made and any possible limitations of the interpreted results

o how the investigation could be extended to provide further results

o what worked well and what didn’t (in terms of the process and calculations)

o any further investigations that could lead on from this one

Bibliography

•    all sources used must be included and referenced appropriately.

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MOEC0021 STA 106 ENGG 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 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