After your resoundingly successful debut at IMC, Inc., the company is clearly eclipsing the number of contracts obtained in its first year of operation. The next contract you have been assigned comes from the famous Rocket Tech Division of Utoff A.F.\ Base, having to do, apparently, with the development of the new space station. The letter you received on the matter follows.
18 October, 1996
Independent Mathematical Contractors, Inc.
Suite 2, Strawmarket Business Plaza
Lonlinc, SK 04685
As you undoubtedly know, the National Space Agency (NSA) is in the process of developing a space station, to be built in orbit in the foreseeable future. After having in the last year capitalized on our success in the development and use of such defensive works as the Otpatri missile system to carefully assess the success of a system to protect the space station from space asteroids and debris, we are faced now with another aspect of the planning for the construction of the space station Omfreed.
In the course of the construction of the space station, it will be necessary to send manned and unmanned Extra-Vehicular Craft (EVC) between different units of the station being assembled. It is initially planned that these units be initially positioned some 500 feet apart. The EVC will move in a straight path between the units, and it is proposed that it move so that its distance from the first unit be given by one of the two formulas
|d1(t) = 30 t (1 - e(-.0458 t)) -
.339 t2|| or|
|d2(t) = 20 t (1 - e(.02 t)) +
where distances are in feet and time t in minutes. The thrust (force) generated by the engines of the EVC is given to be T(r) = .15 r(8/3), where r is the rate at which its fuel is burned. As you also know, the great-great-grandfather of the space program, Isaac Newton, reported that the force on an object is proportional to its mass, m, times its acceleration, a.
We need from your company:
We look forward to receiving your report, which should be typewritten and 3--5 pages in length. Equations explaining your solution should be included in the report, and it is permissible to hand-write these in blank lines between your typewritten explanation if this greatly facilitates the production of the report.
Lieutenant General Rick N. Backer
Commander, Rocket Tech Division
last modified on 18 Oct 1996Gavin's Calc I Project 2, Fall 1996