Light Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 1.8
Distraction
ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Procedure; Human Factors
Aircraft X was descended to 020 and turned to a heading of 190 to be cleared for the visual approach. A few minutes later 2 aircraft departed adjacent airports and needed to be identified and turned on their way. 1 aircraft misheard the instruction to climb and ident so I had to take a longer time to work with him and separate him from aircraft overhead. By the time I went back to Aircraft X he was within a mile of a 2;500ft MVA. I turned him towards the airport and away from the obstruction but he could not report the airport in sight due to a newly formed cloud deck. Aircraft X went into the MVA by about a half mile and was out and turned completely northbound. He landed without further incident 5 minutes later utilizing the GPS approach I should have kept the aircraft at a higher altitude until he saw the airport.
TRACON Controller reported being busy and not catching an aircraft go into a low MVA.