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Motion 2
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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
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Skill 6 of 15
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Equation rearrangement
Previously (in the Throwing & free falling skill) we arrived at these two equations for our flying orangecannon shot orange:
$\displaystyle s_y=v_{y,0}t \frac12 gt^2\qquad$ and $\qquad {s_x}=v_{x,0}t$
Its technical sheet tells a muzzle velocity of $5\,\mathrm{m/s}$. At your shooting angle this could mean $4\,\mathrm{m/s}$ vertically and $3\,\mathrm{m/s}$ horizontally. So, we know the values $v_{x,0}=3\,\mathrm{m/s}$ and $v_{y,0}=4\,\mathrm{m/s}$.^{1} They are not unknowns anymore. In the two equations there are thus only three unknowns left: $s_x$, $s_y$ and $t$.^{2}
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References:
 ‘A History of Mathematical Notations (Dover Books on Mathematics)’ (book), Florian Cajori, Dover Publications, 1st ed., 2011, www.amazon.com/dp/0486677664, ISBN 9780486677668
 ‘Essentials of Logic’ (book), Irving Copi, Carl Cohen & Daniel Flage, Taylor & Francis, 2nd ed., 2016, books.google.dk/books?id=6eAqDwAAQBAJ&printsec=frontcover, ISBN 9781315389011