Simulation of Projectile Motion

Mechanics Academy is partially broken because thinkbot is being reworked. Like a pair of phoenixes, they’ll both rise from the ashes soon. As in eventually.

Remember that at any time $t$, the projectile's vertical and horizontal displacement can be calculated by:

\[\begin{aligned} x & = v_0\, t \cos(\theta) \\ y & = v_0\, t \sin(\theta) - \frac{1}{2}g\, t^2 \end{aligned} \]

Can you find the angle at which the projectile travels furthest when launched at 40 m/s? What if you launched it at 30 m/s? Does the angle change?