PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 115; Flight Crew Total 1100; Flight Crew Type 675
Training / Qualification; Communication Breakdown; Time Pressure
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Unstabilized Approach
Flight Crew Took Evasive Action; Flight Crew Executed Go Around / Missed Approach
Procedure; Human Factors
I was with an instrument student practicing landings; we did a touch and go on Runway 9 at ZZZ and were going to make a full stop landing. We were instructed to make a right traffic pattern and once on the right cross wind I asked Tower if I could land on Runway 5 and hold short of Runway 9 being that I knew there was another airplane in the pattern. Tower then cleared me to land Runway 5 and hold short of Runway 9. My student then made an approach to Runway 5 and ended up bouncing the landing and began to porpoise. As I went to take control the aircraft the student went full throttle to go around. We then climbed to about 80-100 ft. and I looked to our left and the other aircraft was on the departure leg for Runway 9 and we were on a collision course when I kept the airplane in ground affect causing us to pass slightly in front of the other aircraft and below it.
PA28 Instructor reported student go around resulting in a NMAC with crossing traffic.