$1.$ For this problem assume drag force is proportional to velocity squared and g $=10$ m$/$s$2.$ The approximate terminal velocity of a $($theoretical$)200$ kg skydiver is $-55$ m$/$s$.$ A parachute is designed such that the $200$ kg skydiver has a terminal velocity of $-5$ m$/$s$.$ Assume the parachute deployment is instantaneous.$($a$)$ Compute the drag coefficient k of the parachute.$($b$)$ A $200$ kg skydiver has deployed the parachute. State a differential equation modeling the velocity of the skydiver as a function of time. $($Please do not solve yet$)($c$)$ Use the substitution to restate the equation so that height x is the independentvariable. $($Do not solve it yet $...$please.$)($d$)$ At what altitude should the parachute be deployed so that the $200$ kg skydiver is slowed from $-55$ m$/$s to $-10$ m$/$s before landing? $($Hint: NOW you can solve. Use the initial condition v$($x$0)=-55$ together with your equation from $($c$)$ to get a unique solution and then use it to solve for x$0.)$