Points for this task: 25
The Descent Protocol
Premise
You’re a companion of Han Solo, the Millennium Falcon took a hit during a short battle near the ruins of a forgotten Sith outpost orbiting a rogue planet. While escaping, you made the dumb call to jump into an uncharted gravity rift. Now you’re trapped in what appears to be a vertical gravity tunnel, the data does not match anything you seen before. Gravity doesn’t pull in one direction. It changes with time. Your sensors spit out a equation:
\[g(y) = 9.8 \cos(2t)\]The ship’s boosters are offline, and Chewie’s unconscious. Han is piloting manually, he needs your help in finding the trajectory.
Suddenly, your mind is touched by a vision from Master Yoda.
The vision says:
System to save:
\[x(t) = \begin{bmatrix} y(t) \\ v(t) \end{bmatrix}\]With dynamics as:
\[\frac{d}{dt}x = f(x, t) = \begin{bmatrix} v(t) \\ -9.8 \cos(2t) \end{bmatrix}\]You realize you are 10 V (Vectras) above the abyss, the ship is still and each pulse of time is 0.1 seconds.
Use Yoda’s vision to calculate the state ( x ) at ( t = {0.1} ) seconds and save yourself.