Please just answer $12\mathrm{.}116$ and check to see if it aligns with the given answers!

A trebuchet releases a rock with mass $m=50kg$ at the point $O.$ The initial velocity of the projectile is vec$(v{)}_0=(45$hat$()+30$hat$())\frac{m}{s}.$ If one were to model the effects of air resistance via a drag force directly proportional to the projectile's velocity, the resulting accelerations in the $x$ and $y$ directions would be $x^{}=-(\frac{}{m})x^{}$ and $y^{}=-g-(\frac{}{m})y^{},$ respectively, where $g$ is the acceleration of gravity and $=0\mathrm{.}64k\frac{g}{s}$ is a viscous drag coefficient. Find an expression for the trajectory of the projectile.

Problem $12\mathrm{.}116$

Continue Prob. $12\mathrm{.}115$ and, for the case where $=0\mathrm{.}64k\frac{g}{s},$ determine the maximum height from the ground reached by the projectile and the time it takes to achieve it$.$ Compare the result with what you would obtain in the absence of air resistance.

$t_{\text{m}\text{a}\text{x}}=3\mathrm{.}000s,H_{\text{m}\text{a}\text{x}}=49\mathrm{.}21m,$ percent increase in height with no air resistance $=2\mathrm{.}363\%$