After this lesson, why not add the effects of air? It is nearly impossible to do with pencil and paper, but very easy on the computer. Assume that air presents a deceleration on the ball opposite to $v$ given by $a_{air}=Cv^2$, where $C$ is some drag constant like $0.1$.

To use this, we need to know the direction in which the ball is flying at any instant. This is given by $\alpha=\tan^{-1}\frac{v_y}{v_x}$. If we know this flight angle, then the $x$ and $y$ deceleration components will be $a_x=a_{air}\cos(\alpha+\pi)$ and $a_y=a_{air}\sin(\alpha+\pi)$. Let's put this in, given that $\tan^{-1}\left(\frac{a}{b}\right)$ is math.atan2(a,b).

This code will not run. You need to fill in some launch angle $\theta$ in the theta= line and some launch speed in the v= line. You can try experimenting with the drag constant, making it larger or smaller. You might make it $0$ and run it again at $0.01$ to compare the ranges of the two (i.e. it should go farther with no air drag). Dismiss.

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