771 words - 4 pages

PLEASE NOTE: This version is extremely unreadable, YOU MUST LOOK AT THE MS WORD DOC FILE.Rocket Launch PortfolioMr. McAfeeMath 4/Block 17 February 2003By: Ronald K. Ellis IIIThe Rocket LaunchAs the shuttle STS-82 lifted off from the NASA launching pad at Cape Canaveral, Mission Control in Houston was receiving the following data about the vertical velocity of the rocket in feet/sec. We will use this information to give an estimate of the distance the rocket travels in its first 40 seconds.Time since Launch(s) Velocity (ft/sec)002.88445.76998.6416011.5222414.429017.2836320.1644423.0452825.9261028.868931.6876634.5683937.4490340.3296543.2102746.08108748.961146a)Use the data to find the altitude of the rocket after 40.32s (assume the rocket is launched from sea level). Describe your steps and justify your conclusion.The blue area under the curve at a given time value is equal to the altitude at that same time.Calculate the total altitude after 40.32s (Using trapezoid area approximation method)Formulas-Substituting in the rocket launch data to calculate area under curve at time index 40.32sIn this step I used the principle that the area underneath the data points at any given time index is equal to the total altitude at that same time index. This principle is proven when one multiplies the units the seconds unit cancels leaving only distance for an answer.b) Use a full sheet of graph paper and graph the times up to 40.32 seconds. What is the pattern for the points that you found? Find an equation that matches the data as close as you can. (Assume a y-intercept of 0.)The trend is an upward one taking place in 2.88s time intervals.1) Calculating the Median-Median LineI)Split data into three series by smallest values.Series 1Series 2Series 3II)Calculate median values for each series.Summary Point for Series1Summary Point for Series 2Summary Point for Series 3III) Using the two outermost summary points in order to calculate the equation of the line between them.VI) Constructing the line parallel to this line but is one-third of the way to the summary point for Series 2.Graph on separate page.c)Use the equation you found in part (b) to approximate the altitude after 40.32 seconds. How did it compare to part (a)?The answer in part (a) was somewhat lower but not a significant amount. In my opinion the line is still viable to approximate altitudes.d)The ozone layer is between 10km and 50km above sea level. Assuming the velocity continues at the pattern in part (b), find the velocity when the shuttle enters and exits the ozone layer. SHOW ALL WORK. Note: there are about 1.61km in a mile.EvaluationThis projects intent was to insure our overall understanding of area under curve as well as well as different ways to approximate it without knowing calculus. This portfolio is meant also to be used as a precursor to calculus but instead of finding the integral we approximated it using trapezoids and next by graphing a median-median line giving us two fairly good approximations of area.

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