'STEM' Cells

Attempting to aid in the latest educational craze, promotion of STEM Information (Science, Technology, Engineering and Math), we boldly go forth into our own feeble attempts by publishing little cells of wisdom. For a Computer Club, this seems like a worthwhile endeavor.
  1. So, we start with a Math problem that has practical value for "Indiana Jones" types wandering the globe. Go down to Math.

  2. Next, we consider Computer Science, which is in the TECHNOLOGY bailiwick. This could be an introduction to cryptography or an exercise in computer programming, whatever your interests. Scroll down to Technology.

  3. Now it's time for some Science, rocket science to be specific. This problem relates to classical physics and moving bodies in a gravity field. No need to consider Einstein or general relativity, we won't be moving that fast. Roll down to "Focus on Science".

Answers to these problems will appear on the Members Page, available to Members after they log in. Most of the site is accessible without logging in.

Focus on SCIENCE

General question: Are Computer Science and Rocket Science really Sciences?


4/15/2014 First Science Problem
The current topic is rocket science, arguably a 'science' discipline. And within science, we specifically address classical physics, looking at one aspect of physics addressing the science of moving bodies.

A rocket ship will be launched by Acme Rockets Inc. or was it AJAX Rockets, but funded by NASA, CIA, NSA, DIA, FBI, DOE, DEA, DNI, NGIA, NRO, DHSIA, USAF, NCIS, ATF, S.H.I.E.L.D., S.P.E.C.T.R.E., and C.A.O.S. with the goal of reaching the first LaGrangian Point L1 between Earth and Sun. The total weight of rocket ship and payload is one million pounds. The engine has been specially designed to produce two million pounds of thrust, remaining perfectly constant throughout the voyage until shut down manually. This phenominal performance is possible through advanced feedback control systems, chemistry of tachyons and dilithium crystals, and high performance computer technology.

The question is can this rocket ship reach the first LaGrangian Point above Earth within an initial 1-hour window? Management wants to know. With all of the funding coming in, this might be important.

Overview: The rocket ship, weighing 1 million pounds on the ground, is propelled with a rocket engine producing a constant 2 million pounds of thrust. Gravity at Earth's surface is pulling the rocket ship down with 1 million pounds of force (since it has a mass of 1 million pounds).

Assumptions: Assume the whole rocket ship loses a negligible amount of fuel per minute while it is thrusting. Also assume the rocket ship goes straight into outer space without attempting to orbit the earth. Also assume the rocket ship can reverse thrust immediately upon reaching the desired distance. Also assume the pull of gravity remains constant till the destination (the most egregious assumption). These assumptions make the whole calculation an approximation, but a ballpark number is needed for management. The crew, a group of Space Cadets on their second training mission, will be customizing the operating parameters during the flight. A mid-course correction may be required. The full payload is classified, and if we told you what it was, you know what we'd have to do.

As a bonus, just for management, compute the velocity of the rocket ship at its destination. Later, please consider removing most of the above assumptions and provide a "best judgement" answer. Show your work.



Focus on TECHNOLOGY

Cryptography, the encoding and decoding of messages, involves math and programming. One without the other is worthless, unless you are using a very simple form of encoding. There are two paths to data security: 1. Develop complex algorithms that no one but the inventor can figure out, or 2. Use well-known algorithms but use very long cryptographic keys to encode and decode messages. The world today predominantly favors path 2. Being nonconformists, we will investigate path 1 since it involves very little math.

The following paragraph is an encoded cipher text which you are to decode. Copy and paste it into your own text file so you can work on it.

\rxu plvvlrq/ li |rx fkrrvh wr dffhsw lw/ zloo eh wr euhdn wkh frgh ri wkh Jhupdq Hqljpd Pdfklqh1 Lw zrq*w eh hdv|1 Wkh ehvw plqgv lq wkh fu|swrjudsklf zruog kdyh fudiwhg d iruplgdeoh p|vwhu| pdnlqj dssdudwxv1

The algorithm you will need is very old and is known as Caesar's Cipher. Check it out in your Funk & Wagnals, or whatever you use. Write a program to make it less tedious using any programming language you prefer. For you cryptographers out there, give the newcomers (like me) a chance to figure it out before you ignite the flames of ridicule. This is meant as a programming problem, not a way to hack the NSA.

One or more solutions will be shown in a few weeks on the Members Page. And, for members decoding the message, please log your answer into the Members Forum. If you would like to make your version of Captain Midnight's Super Decoder Ring, go for it. Just make enough for the whole club. Maybe we could use it for secret messages between members, which would hamper the NSA in monitoring our activities.



Focus on ENGINEERING

Computer Science certainly involves Hardware Engineering and Software Engineering. But is it a science?



Focus on MATH

10/9/2013: Intrepid explorer Professor Wexler (www.wexClub.com) was surprised as he stumbled on a partially buried pyramid while trekking through the Sahara about 100 miles west of Giza. This hitherto unknown pyramid had recently been blown mostly free of sand by the sirocco that haunts the area. Having only his bowie knife and his surveyors chain in his old kit bag, he did his best to obtain some measurements of this gigantic find.

He wondered how tall this behemoth was, but had no scafolding to facilitate this measurement. However, remembering some math from his days at The Sorbonne, he figured he could calculate it. So, clearing away sand from the base, he found it to be square. Staking one end of his chain with his knife, he found the base to be a perfect 4-sided square, with a length shown below. Knowing that the height could be calculated once the length of an edge, from one of the 4 corners to the sharp-pointed top, could be found, and being nimble and a bit wiry, he staked his chain at a corner and scrambled up to the top. The edge measurement is shown below.

From the two measurements, he quickly calculated the vertical height from ground level. If you are the first to do the same and post the answer (to 2 decimal digits) on the NOCCC Member's Forum, you will win a free raffle ticket at the next main meeting. If you want to include diagrams, compose a Word Doc and email to webmaster@noccc.org. The solution to this problem will be posted on the Member's Page in a month.


The Pyramid Math Problem

diagram of pyramid

c is 800 feet (the base length) and b is 900 feet (an edge length);
calculate h

The base of the pyramid is a perfect square, with a base length of c. The edge from a base corner to the top has a length of b. The vertical distance from ground level to top has a height of h.