PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Private; Flight Crew Flight Instructor
Troubleshooting; Workload
Aircraft Equipment Problem Critical
Air Traffic Control Provided Assistance; Flight Crew Returned To Departure Airport; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Landed in Emergency Condition
Aircraft
I was performing a training flight under an IFR flight plan with my student.We were taking off Runway XXR at ZZZ all engine instruments were in the green; after 100 ft. we start to feel roughness. I took the controls from the student and initiated a right turn to make it to Runway XY. During the turn I was able to climb and maintain close to 200 ft. I then decided to land on any suitable runway at that time. We eventually landed on the midsection of Runway XXR; close to the XX taxiway. After landing and exiting the runway to Taxiway XX; I tried to start the engine to taxi back to the ramp; but wasn't able to so I contacted Ground Control and Maintenance towed the aircraft to the ramp.During the entire event and us being at a very low altitude; we did not monitor the engine parameters as we were focused on landing the aircraft safely.
PA-28 Instructor reported engine failure on departure during a training flight.