B737-800
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 9
Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance
Human Factors
I was working North Radar. Aircraft Y was on a visual approach; switched to the tower and short final. Local had Aircraft X in line up and wait and cleared for takeoff. Aircraft Y had to go around due to the other [carrier] not rolling.Aircraft X came off runway heading first; Aircraft Y went around right behind him. Tower had issued a 250 heading to Aircraft Y in trail. Targets were close. Tower switched both at the same time I believe; there was some confusion on the departure frequency and I had other aircraft I was working making transmissions.In my opinion; the targets were merging as the go around aircraft was faster than the departure aircraft. I turned Aircraft Y further south to 180 heading to avoid a conflict with Aircraft X which was being over taken.Aircraft X also took the turn to 180 so both aircraft were turning. I sorted out the confusion; turned Aircraft X back to the west and had to climb Aircraft Y to 040 and turn back to the southwest to avoid Aircraft Z on final to LCK. Tower had no other departures nor was there anyone else on final. Don't use the squeeze play. Further the departing Aircraft X should have been turned northwest with the go around behind turning southwest to separate faster.
CMH TRACON Controller reported a loss of separation when a departure and a go-around got too close.