This hanging math drawback shared by an nameless reader is taking the web by storm. This hanging math drawback, also referred to as the overhead line curve, was allegedly posed throughout an Amazon interview. Nevertheless, the issue is far older and was first found by Robert Hooke within the 1670s. The equation was derived in 1691 by Leibniz, Huygens and Johann Bernoulli.
The catenary curve has a U-shaped form, which on the floor resembles a parabolic arch, however isn’t a parabola. It’s a curve that an idealized hanging chain or cable will assume underneath its personal weight if solely supported at its ends. Overhead traces and associated curves have many different makes use of as effectively, together with structure and engineering (e.g., within the development of bridges and arches in order that forces don’t create bending moments).
For instance, within the offshore oil and fuel trade, “overhead line” refers to a metal riser, a pipe that’s suspended between a manufacturing platform and the seabed and takes on an approximate catenary form. Within the rail trade, it refers back to the overhead line that carries electrical energy to trains.
Beneath is the query. See when you can resolve the query.
“A cable 80 meters lengthy hangs from two masts, each 50 meters above the bottom. What’s the distance between the 2 poles (as much as a decimal level) if the middle cable is (a) 20 meters above the bottom and (b) 10 meters above the bottom? “
(b) 10 m above the bottom
Be aware: The answer to the primary query (a) is described in Chatterjee and Nita (2010) and requires some data of arithmetic or physics. For (b) you have to assume past the mathematics formulation. Query (b) appears to be like complicated however is far simpler to resolve with out utilizing a math formulation. All you want is easy logic with just a little thought.
Beneath is a video on methods to resolve the 2 issues.