I need help with problem $12\mathrm{.}116$

Problem $12\mathrm{.}115$

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.

Figure P$12\mathrm{.}115-$P$12\mathrm{.}118$

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.