Parabola Equations

[Ether]

Given the coordinates (0,h) of the launch point and (xp,yp) of the apex, find the equation of the parabola.

[Aaron.Graeve]

I give Ether my highest complements. It takes a certain kind of problem for me to voluntarily work on it for about 4 hours. I worked through the 1st, 5fth, and 6th sub-problems relatively quickly, but the middle three are what are stalling me. I have attempted to solve sub-problems 3 and 4 using both systems of equations and using matricies with Cramer's rule. My system of equations was having sign issues (more than can be expected considering I am comparing my solution to Ether's) and my matricies were not working from my rustiness in this area. I will continue to work tonight and post if anything changes.

Once again, props to you, Ether.

[Aaron.Graeve]

I just finished up the solutions problems in the original post, using three pages of paper in the process. Ether, your solutions check out fine to me (albeit I have very well could have missed something). I also see what you mean by the solution being messy. I think the derivation was messier. To anyone wondering, I solved it each time with a set of matrices and Cramer's Rule. Cramer's rule is both really cool and useful. I advise you all to go check it out. I may try my hand at proving the others tomorrow. Ether, as I stated previously, this is a very good challenge. Thank you.

[TRWSHSHLX]

Just finished up all the problems and everything checks out!

I solved most of them using row reduction then the rest were solved using MATLAB. For anyone that's currently taking a class or looking for a refresher in matrices or 2-d kinematics, try these problems out!