Calculating a trajectory
I purchased a new cannon rig, which can accommodate greater, perhaps even dangerous, amounts of propellant. Since there are so many variables involved, I need to find the optimal solution for maximizing the distance traveled. To do this, I will vary the angle of launch (0-90 degrees) and the amount of propellant (0.05-0.12 kg). While I may have some suspicions about the best-case scenario, I will adopt a hill-climbing procedure to ensure I find the globally optimal solution.
This problem is convex, meaning that a hill-climbing approach should be able to find the globally optimal solution. Therefore, it is a great candidate for this optimization technique.
I will start with an initial guess of 0.05 kg for the propellant mass. The starting height will be 5 m, and I will assume an acceleration due to gravity of g = 9.8 m/s^2. The starting angle will be 0 degrees. I will treat drag and the z and y components as in hw1e, as well as collision with the ground.
It's worth noting that the physics in hwbe were a bit off. The calculation for the force in the xz-direction was specified there as F = Cpv, but it should rather have been based on the component of total velocity, F = Cpv^2. This means that if you have a line like
-e.5rho*C*A/massvx[j-1]*2
you should replace it with something like
np.sqrt(vx[5-1]**2 + vy[1,5-1]**2) * ax - (.5*rho*C*A/mass) * v**2 * (vx[i,5-1] / v)
for hw11. You will need to perform this transformation for the y-component as well.
First, define a figure-of-merit function dist(angle, n_prop) which accepts the angle of launch and the mass of propellant used (in kilograms) and returns the distance traveled (in meters). This will be very similar to much of your code from hve. You may also use the reference answer from hxe to compose dist. A reference case for dist is:
assert np.isclose(dist(38, 0.16), 134.7136)
Your solution should include a function dist.
