Ch$\mathrm{.}2$ exercise $3$ from "Numerical Methods for Physics" second edition $($MATLAB$)$ by Garcia.

The balle program overestimates the range and time of flight $($Figure $2\mathrm{.}4).$ Fix this bit of sloppy programming: Compute a corrected maximum range and tame of flight by interpolating between the last three values of $r$ using the intrpt function from Section $1\mathrm{.}4.$ Measure the improvement in the computed range and time of llight when there is no air resistance. Take an initial height of $0m,$ initial speed of $50\frac{m}{s}.$ angle of $=45,$ and try a variety of values for the time step $7.[$Computer$]$