Air carrier flight crew reported a NMAC while taking off. The crew was cleared for takeoff while another aircraft was cleared to land on an intersecting runway. The tower controller; realizing the mistake; instructed the landing aircraft to go-around. As the landing aircraft commenced go-around the air carrier crew reported they flew 300 feet under the go-around aircraft.
Synopsis
Air carrier flight crew reported a NMAC while taking off. The crew was cleared for takeoff while another aircraft was cleared to land on an intersecting runway. The tower controller; realizing the mistake; instructed the landing aircraft to go-around. As the landing aircraft commenced go-around the air carrier crew reported they flew 300 feet under the go-around aircraft.
Narrative
ZZZ Tower cleared us to line up and wait on Runway XL for an Aircraft Y on a 4 mile final for the crossing Runway YZ and then cleared us for takeoff on XL after only sitting for about 30 seconds. We couldn't see the Aircraft Y because it was in both of our blind spots so we assumed the controller had the proper spacing to make it work. Right before we hit 80 knots I made visual contact with the Aircraft Y converging with us. As we reached V1 I realized that we were on a perfect collision course with the traffic at the runway intersection. We couldn't reject as we were reaching V1 and if they didn't go around and we rejected we would've hit them on the runway no doubt; but at that moment ZZZ tower called up with collision alarms blaring in the background telling them to go around as we rotated. I out loud confirmed that the Captain had them in sight to begin maneuvering under them. However now we were both climbing for the exact same point in the sky and ZZZ Tower began yelling for us to level at 1;000 feet and both to turn; us left and them right only to switch the directions up a few seconds later realizing his mistake. We flew directly under the Aircraft maintaining visual separation and broke into a right turn. We later looked at a playback on the ground in ZZZ1 and found that we missed each other by about 300 feet. The Captain maintained aircraft control the entire time and never stopped flying the airplane. I attribute the outcome to excellent CRM and a phenomenal Captain. We complied with vectors and reconfigured the aircraft and continued the rest of the flight with no issues. Tower apologized in their final remarks to us and took full credit for the incident.
Second reporter narrative
At around XA00 we were taking the Runway XL in ZZZ 'line up and wait' we were advised that Aircraft Y was on a 4 mile final landing Runway YZ and additional traffic crossing downfield. We were given the clearance by tower ' Aircraft X Runway XL fly heading 080 cleared for takeoff'. We took off at the same time tower had instructed 'Aircraft Y go around; go around and climb hard; climbing right turn please.' They had instructed us as we were taking off to maintain in 1;000 feet and to make a left turn 'hard left turn' then shortly after that clearance tower amended that and instructed us to make a right turn (which I think we were both thinking was the safest course of action at the time). After the traffic was no longer a factor anymore tower said on frequency ' Aircraft X that was all my fault there; climb and maintain 5;000 feet and go back to a heading of 080'. That was a little too close for comfort and left me feeling extremely uneasy the whole flight. We proceeded to ZZZ1 without any further incidents. Pay closer attention to all the crossing/landing/take-off clearances while lining up and waiting and when cleared for take-off. I am pretty good at doing that usually but that night I had lost track of who was who and who was were.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.