## Lesson goal: Animate a projectile in flight with simple physics

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As in this lesson you saw how a single pixel could be moved straight across the screen. Of course one of the challenges of making an animation is in determining what should guide the object in how it moves. In other words, where should the object be drawn from one moment to the next? Well in things like video games and movies, the objects are made to move according to the laws of physics. Let's do that here.

Basic physics allows one to predict how a ball will fly through space (with no air in the way). If you launch the ball from position $(x,y)$ with a speed of $v$, at an angle $\theta$ with the ground, then the ball will be at a new $(x,y)$ coordinate some $\Delta t$ in the future according to (given that $v_x=v\cos\theta$ and $v_y=v\sin\theta$): $$x=x+v_x\Delta t$$ and $$y=y+v_y\Delta t+\frac{1}{2}g\Delta t^2.$$ Although $v_x$ will stay the same throughout the flights, $v_y$ will change via $$v_y=v_y+g\Delta t.$$ In all of these equations, $g$ is the acceleration due to gravity, which is $9.8$m/s$^2$ on earth. Here is some code that will make a pixel fly through an airless world. See if you can fix it up and get the little ball to fly!