Motion 2

TechnicalMotion equations

Throwing & free falling

MathematicalPythagoras' theorem

HistoricalPythagoras of Samos

MathematicalSquare root

Equation rearrangement

Equation manipulation

Rules of algebra

Graphs

Linear & parabolic

TechnicalTurning & speeding

Circular motion

Elliptic motion

Centrifugal effect

EndingSummary of the Motion discipline
Participants9
Let’s rearrange some more:
$$\begin{align}
s_y&=v_{y,0}\left(\frac{s_x}{v_{x,0}}\right)\frac12 g \left(\frac{s_x}{v_{x,0}}\right)^2\\
&=\boldsymbol{\frac{ v_{y,0} s_x}{v_{x,0}}}\frac12 g \left(\frac{s_x}{v_{x,0}}\right)^2 \\
&= \frac{ v_{y,0} s_x}{v_{x,0}} \frac12 g \boldsymbol{\frac{s_x^2}{v_{x,0}^2}}
\end{align}$$
Here, in the first step, we moved $v_{y,0}$ into the bracket and to the top (numerator) of the fraction. Because, the numerator counts how many there are of the fraction, and multiplying it with a number does the same thing. It seems to be a general rule, which we could write as:
$$a\left(\frac bc\right)=\frac{ab}c$$
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