Hint:

The key here is to apply the (x-direction) linear momentum theorem to a control volume chosen so that the force you want to determine acts somewhere on its boundary, and everything else you need is either given or can be determined. One such CV could be bounded by a line just outside the exit plane going down to just above the floor, then leftward just above the floor, through the hinge to the atmosphere, then up above the system, and horizontally rightward back to where you started. Another could be the same CV as recommended in the hint for (a), with some argument for how the x-force on the hinge is transmitted to the CS.