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    Machinedesign 1805 Pi Ski396 0 0
    1. Automation & IIoT

    Fun with Fundamentals: Problem 192

    March 1, 2000
    Getting to the root of a problem can clear up areas of doubt, as this month’s problem by Steve Zhang of Aloe, Ore., demonstrates
    Motion System Design

    π in the sky

    Motionsystemdesign Com Images Pi In The Ski396

    Problem 192 — Getting to the root of a problem can clear up areas of doubt, as this month’s problem by Steve Zhang of Aloe, Ore., demonstrates.

    Deep in the Pentagon, a highly classified meeting between the joint chiefs of staff and their new radar supplier was in progress.

    “I’m pleased to announce we’ve found a radar net system that’s both cost-effective and fully functional,” stated Brig. Gen. Brass. “Without further ado, here’s Mortimer Blynd of Tri-Gen/Git-Rite Inc.”

    “The new Failsafe Radar Integrated Tracking System (FRITS) consists of four towers that each have a sweep radius of 10√3 miles ,” stated Blynd. “These towers (A, B, C, D) form a square, (see diagram), with an area of 900 square miles. Together, *ahem*, with some negligible overlap and one very small blind spot, *ahem*, they can monitor this area.”

    Given the measurements stated, what is the area of the blind spot? Can the enemy hide a tank or a munitions plant in it?

    Technical consultant, Jack Couillard, Menasha, Wis.

    Solution to last month’s problem 191 — Your ETA is right on target if you answered Lottie and her boyfriend get wet. Here’s the watered-down analysis:

    First, let’s find out if the water balloon will strike the Ferris wheel or pass over it.

    Let:
    y1 = Maximum height attained by the water balloon, ft
    t = Time from launch to maximum height, min
    x = Horizontal distance from launch point to the point directly beneath the balloon’s zenith, ft
    v0 = Initial velocity of water balloon, given as 60 fpm
    Φ = Water balloon launch angle, given as 60 deg
    g = Acceleration due to gravity, 32.2 ft/sec2

    From physics, we know that the time it takes a projectile to reach its zenith is:

    Motionsystemdesign Com Images Fun Equ 1 396

    The balloon’s maximum elevation is:

    x = v0(cosΦ)t = 48.4 ft (1)

    The horizontal distance the water balloon has traveled at this time is:

    Motionsystemdesign Com Images Fun Equ 2 396

    Since the closest point of the Ferris wheel is 55 ft away, the balloon is descending by the time it reaches the unsuspecting couple. At this point you can draw a diagram to scale and note that the balloon strikes the wheel at a horizontal distance between 65 and 70 ft. Use (1) to find that the time is between 2.16 and 2.33 sec.

    The Ferris wheel turns at 1 rpm, so between the time frame allotted, the wheel has turned 13 or 14 degrees in its rotation. Lottie and company are clearly the ones in the line of fire.

    Contest winner — Congratulations to Joe Kohler of Cleveland, who won our January contest by having his name drawn from the 11 contestants who answered correctly out of a total of 32 entrants for that month. A TI-85 calculator is in the mail to him.

    The TI-85 Graphing Calculator from Texas Instruments solves for any variable in an equation, can solve 30 simultaneous equations, and finds the roots of a polynomial up to the 30th order. It handles complex numbers in addition to matrices, vectors, lists, and strings. You can perform graphic investigations of almost any type of problem — functions as well as parametric, polar, and differential equations.

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    Fun with Fundamentals: Problem 191

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