Graphs

An equation for a motion is, shall we say, not exactly visually pleasing. Just a ‘mathematical description’ or ‘recipe’ – or model – of a motion. It can give us numbers. But we can’t see it.

Let’s invent a way to “see” a mathematical description.

The motion equation $s_y=\frac{v_{y,0}s_x}{v_{x,0}}-\frac12 g \frac{s_x^2}{v_{x,0}^2}$ may look rather huge, but the only unknowns are $s_x$ and $s_y$. We already tried to plug in values for $s_x$ and then we got matching values for $s_y$. When $s_x=1\,\mathrm m$ was plugged in, $s_y=0.33\,\mathrm m$ came out. This is a point, a coordinate set $(1\,,\,0.33)\,\mathrm m$, which we can easily draw as a dot in a coordinate system: