Fun with Fundamentals: Problem 217

July 1, 2000
Being out of your depth can leave you short, as this month's problem by David C. Branch of Radford, Va., demonstrates

In the hole

PROBLEM 217 – Being out of your depth can leave you short, as this month's problem by David C. Branch of Radford, Va., demonstrates.

Finagel J. Wurme strode confidently among the scurrying workers at the Schatter Glassworks Co. They were lowering a new 500-ft deep storage tank into the hole that the newly formed Wurme Contractors Inc. had dug for them. Wurme, who had been paid cash up front for the project, was inspecting his work and making insinuating comments on future business with the foreman.

As the two walked and talked, the foreman accidently kicked a medium-sized rock into the pit. (Assume the rock had no vertical velocity.) Six seconds later, both men heard the rock hit bottom. The foreman thought a minute, grabbed Wurme, and held him over the pit. Using 1,100 fps as the speed of sound and 32.2 ft/sec2 as the acceleration due to gravity, how deep is the pit? Where should Wurme be dropped?

SOLUTION TO LAST MONTH'S PROBLEM 216 -- You think on your feet if you answered one. Here's how Bluff became the man of the hour.

Bluff numbered the boxes 1 to 10. He took one bolt from box 1, two bolts from box 2, three bolts from box 3, and so on, up to 10 bolts from box 10. He put all 55 bolts on the scale. Since the customized bolts weighed 1 gram less than the standard bolts, he knew that if the weight was 6 grams shy of 55 oz., then box 6 held the customized bolts. The number of grams less 55 oz. told which box the customized bolts were in.

After delivering the bolts, Bluff helped himself to coffee, also.

CONTEST WINNER – Congratulations to Gerd R. Alzuhn, P.E., of Milwaukee who won our May contest by having his name drawn from the 230 contestants who answered correctly out of a total of 336 entrants for that month. A Maple V Release 5 mathematics software package is in the mail to him.

Maple V Release 5 is an interactive computer algebra system that provides a mathematical environment for manipulating symbolic algebraic expressions, arbitrary-precision numerics, graphics, and programming. Its library features over 2,700 functions that are used in many scientific and engineering applications. Features include a MATLAB link, which lets users execute MATLAB commands from inside the software; a spreadsheet function in which Maple V operations can be performed; and an HTML export function to create web pages. The software is available in Windows 95, Windows NT, Windows 3.11, Macintosh, Power Macintosh, plus UNIX and Linux platforms.

This month's problem submitter receives an EL-546L Direct Algebraic Logic calculator from Sharp Electronics. The EL-546L has an extralarge, 10-digit, two-line LCD display that lets you see the full equation on one line and the answer to the equation on the other. An algebra and playback function enables you to enter an equation and substitute numeric values or correct errors. Another feature is the full-term equation entry function, which enables the calculator to display a fraction equation exactly as it appears in a textbook. The EL-546L has dual power and can automatically switch from solar to battery power in low light.

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