\section{Discussion of results}
As expected, with the increase in polynomial degree error of the solution decreased and condion number of Gram's matrix increased. The most interesting part is how for polynomial of degree \textbf{10} the error got significantly lower, $10^{-12}$ times lower than for polynomial of lower degree, with only around 100 times bigger Gram's matrix condition number, and then for polynomial of degree 11, the error become much much higher and so did Gram's matrix. I suppose that since we get 11 data points, approaching number of data points with the degree of the polynomial lowers the erorr until we have the same polynomial degree as data points at which point the error increases again.






\chapter{Determine trajectory of the motion}