The Birth of Science by Alex Ely Kossovsky

Author:Alex Ely Kossovsky
Language: eng
Format: epub
ISBN: 9783030517441
Publisher: Springer International Publishing

Here the horizontal line AB represents a physical flat plane on which an object is carried uniformly from A to B and then continues beyond B over empty space where it starts falling naturally downward due to gravity, tracing the perpendicular BN as well. The object is traversing the points A → B → I → F → H, and so forth.

All the segments AB, BC, CD, DE are of equal horizontal length, hence each segment corresponds to an identical duration of time needed to traverse it horizontally, and which shall be arbitrarily defined as the unit of time here. As the body starts falling from point B downwards, the vertical components of the motion for the segments CI, DF, EH, are increasing according to the established relationship DT = (A/2) * (TT)2, as discussed in Chaps. 19 and 20. It follows that:

CI = (A/2)*(1)2 = (A/2) * 1

DF = (A/2)*(2)2 = (A/2) * 4

EH = (A/2)*(3)2 = (A/2) * 9

PQ = (A/2)*(N)2 = (A/2) * N2 (in general)

In addition to defining parabola in terms of a Conic Section; a parabola can also be described as a graph on the Cartesian Plane of a quadratic function such as Y = X2, or more generally for X and Y relationship of the form Y = AX2 + BX + C.

Indeed, the modern projectile motion formula for the vertical height as a function of time T, for a body starting at a certain initial height HINITIAL, with zero initial vertical velocity (namely shot directly across with 0° angle horizontally) is:

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