EMB ERJ 170/175 ER/LR
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Communication Breakdown
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Procedure
Departed Runway 8 in ZZZ on the ZZZZZ 3 RNAV departure and had just turned north after ZZZZZ1 when we got at notification from departure control that there was traffic behind us. The traffic was Aircraft Y. We couldn't see the traffic but had them on TCAS. Immediately after we got a TCAS RA warning to descend. TCAS scope was set to 2.5 mile ring and we saw the target inside near our tail 200ft below. Departure control had issued several instructions to the incoming traffic and we heard their acknowledgment that they had us in sight but they kept encroaching on our tail. We also had rising terrain directly to our right side which was the only direction we could go to avoid Aircraft Y. We continued to follow RA guidance until clear of the conflict and proceeded on course shortly thereafter without incident to ZZZ1. Upon later calling TRACON; they said their radar showed 1nm separation while ours showed 200' suggesting they are probably more accurate than us. Nevertheless the traffic should've never been where they were at that time. Aircraft Y departed Runway 8 in ZZZ directly behind us; ignoring multiple ATC instructions; flying directly at us; causing loss of separation and us to execute a TCAS Resolution Advisory to avoid them. Wait longer before clearing GA traffic to takeoff behind scheduled carriers on instrument departures; especially GA pilots that are presumably inexperienced to be flying turbine/high-performance aircraft in a radar environment; especially on weekends.
[Report narrative contained no additional information.]
EMB-ERJ flight crew reported a NMAC with a turboprop resulting in executing a RA.