(Solved): A trebuchet releases a rock with mass m=50kg at the point O. The initial velocity of the projecti ...

A trebuchet releases a rock with mass $$m=50\mathrm{kg}$$ at the point $$O$$. The initial velocity of the projectile is $${\vec{p}}_0=(45i+30\mathrm{j})\mathrm{m}/\mathrm{s}$$. 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 $$x=?(?/m)\stackrel{?}{x}$$ and $$\ddot{y}=?g?(?/m)y$$, respectively, where $$g$$ is the acceleration of gravity and $$?=0.64\mathrm{kg}/\mathrm{s}$$ is a viscous drag coefficient. Find an expression for the trajectory of the projectile. Problem 12.116! Continue ? Prob. 12.115 and, for the case where $$?=0.64\mathrm{kg}/\mathrm{s}$$, 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. $$t_{\max }=3.000\mathrm{s},H_{\max }=49.21\mathrm{m}$$, percent increase in height with no air resistance $$=2.363\%$$