Motion System Design

# Fun with Fundamentals: Problem 218

### Mirror image

PROBLEM 218 – What goes up doesn't always come down on target, as this month's problem by Stan Gardner of Baldwin Park, Calif., demonstrates.

Once again a parade of minivans graced the driveway of Phineas Gotrocks, Esq. He had hired none other than Rufus McSnee, the most expensive interior designer in town, to redecorate his party room.

McSnee was never in the same place for a minute. As Gotrocks raced to keep up with him, McSnee chattered on and on about the many costly appurtenances. "And-and-and we'll have the pink ostrich feathers over here and-and-and the marble-top bar over there ..."

The piece de resistance was a laser, mounted with its output 100 ft below the ceiling. Its beam would strike a mirror on the ceiling and bounce back down to a reflective bowl on the other side of the bar.

As the diagram shows, the bowl was 140 ft from the laser, and the bowl is 60 ft from the ceiling. Find the horizontal distance the mirror should be from the laser's output to make sure Gotrock's summer bash doesn't draw the fire department.

SOLUTION TO LAST MONTH'S PROBLEM 217 – You can sound things out if you answered 496 ft. Here's how Wurme's profits plunged.

Let:

t = Time from the dropping of the rock to when the sound of the rock hitting bottom reaches both men's ears, given as 6 sec.

s = Depth of pit, ft

g = Acceleration due to gravity, 32.2 ft/sec2

v = Velocity of sound, given as 1,100 fps

t is comprised of two components, the time it takes the rock to reach the bottom of the pit and the time it takes the sound to travel upward. From physics, we know that s =½gt2 for falling bodies starting from rest and s = vt for sound traveling through air. The equation for t is then:

With due consideration, Wurme changed his payment policy!

CONTEST WINNER – Congratulations to Gary Shaw of Del City, Okla., who won our June contest by having his name drawn from the 68 contestants who answered correctly out of a total of 140 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 extra-large, 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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Fun with Fundamentals: Problem 217

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