Mathematics Project Paper

The Problem: 1. A toy rocket is launched from the top of a building 92 feet tall at an initial velocity of 186 feet per second. The position at time t is given by ()=−162+0+0 and the velocity at time t is given by ()=−32+0 where 0 is the initial velocity and 0 is the initial height. a) Give the function that describes the height of the rocket in terms of time t. b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet. c) For what time interval will the rocket be more than 250 feet above ground d) After how many seconds will it hit the ground? Next, using the velocity equation, a) Find when the velocity is 0. b) What is the height when the velocity is 0? Does this have any significance? c) Suppose ()=−0 . Solve for t in this case. In particular, find t when 0=186 / . What is the height of the object at this time? Relate this t to the time of maximum height. Describe how this relates to the path of the object. d) What is the velocity when the object hits the ground? Compare to the initial velocity.
The Paper: You are to write a 2-3 page paper describing how you solve this problem, as well as the detailed solution with appropriate calculations. All pertinent computations should be included on a separate attached sheet (an appendix) which you refer to in your paper. In addition, a sketch of the functions s(t) and v(t) are to be included, with descriptions of each graph, and the relationship of the graphs to your results. All graphs should have appropriate scaling. You are to use material from College Algebra in order to complete this task. Cite your text.
The Rubrics: Your paper will be scored on 5 rubrics, listed below. Each rubric will be worth 10 points.
______1. Introduction and Conclusion: Full description of the problem. This includes the
setting, questions posed, and any background information that is relevant to solving
the problem. Well written conclusion citing computed results and any conclusions.
• Well written description of the problem being explored, including a detailed description of the questions to be discussed and solved in the paper: 6-10 pts.
• Cursory statement with little depth, no descriptions: 0-5 points
______2. Addressing Assumptions Involving the Problem and Mathematical
Representation of Problem Information: Full description of the
mathematical elements needed to solve the problem and a detailed description of
procedures used. Competent conversion of relevant information using the
assumptions into appropriate and desired mathematical expressions (equations,
graphs, etc.) as it pertains to the problem:
• Description of core mathematical elements related to the problems and appropriate conversion into mathematical forms (equations, graphs, etc.)
Specifically addresses the assumptions involving the core elements used,
providing supportive reasoning for why the assumptions are appropriate.
Competent conversion of relevant information into an appropriate and desired
mathematical portrayal as it pertains to the problem at hand: 6-10 points.
• Failure to acknowledge all appropriate mathematical elements and/or failure to
properly outline solution procedure for problems: 0-5 points.
_______3. Performing Calculations to Determine the Solution to Problems Posed.
Calculation of the numerical solutions to the problems.
• Correctly performs required calculations necessary to the solution of the
problem at hand. Works with Rubric 2 to insure that proper procedure is
followed. Calculations attempted are essentially all successful and are sufficiently
comprehensive to solve the problem: 6-10 points.
• Incorrect/Incomplete Calculations: 0-5 points.
_______4. Apply and Analyze Information Related to Problem Solutions:
Analyzing the Numerical Results.
• Analysis of the results of the numerical computations, using mathematical
theory and best practices as supporting evidence of the determined conclusions.
Use of the quantitative analysis of the data as a basis for competent judgements,
drawing reasonable and appropriately qualified conclusions from the data or
numerical results: 6-10 points
• Incorrect, inaccurate, or incomplete analysis.: 0-5 points.
_______5. Interpreting the Information Related to the Problem Solutions:
Description of Numerical Results.
• Provides accurate explanations of information presented in mathematical forms.
Includes proper units in numerical results. Interprets numerical results into a
framework that invokes a relationship to “real-world” understanding/physical
reality: 6-10 points.
• No interpretation, lack of proper units, lack of description of results as they
relate to the problem’s framework. 0-5 points.