Machinedesign 1805 Pi Ski396 0 0

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

π in the sky

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.

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:

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:

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.

Related Article

Fun with Fundamentals: Problem 191

Sponsored Recommendations

The Digital Thread: End-to-End Data-Driven Manufacturing

May 1, 2024
Creating a Digital Thread by harnessing end-to-end manufacturing data is providing unprecedented opportunities to create efficiencies in the world of manufacturing.

Medical Device Manufacturing and Biocompatible Materials

May 1, 2024
Learn about the critical importance of biocompatible materials in medical device manufacturing, emphasizing the stringent regulations and complex considerations involved in ensuring...

VICIS Case Study

May 1, 2024
The team at VICIS turned to SyBridge and Carbon in order to design and manufacture protective helmet pads, leveraging the digitization and customization expertise of Toolkit3D...

What's Next for Additive Manufacturing?

May 1, 2024
From larger, faster 3D printers to more sustainable materials, discover several of the top additive manufacturing trends for 2023 and beyond.

Voice your opinion!

To join the conversation, and become an exclusive member of Machine Design, create an account today!