Light Transport
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action; Flight Crew FLC Overrode Automation
Procedure
With an aircraft on a 10 mile final for runway 15; tower instructed us to line up and wait runway 33. After a delay of approximately 30 seconds; we were cleared for takeoff. Shortly after liftoff; tower instructed us to turn right to a heading of 343 degrees which we complied with immediately. Right before FRA (flap retraction altitude) we got a TCAS RA 'descend; descend.' The pilot flying started a descent and we noticed the aircraft on final for runway 15 was 0.5 miles away or less and approximately 500' above our present altitude. The TCAS RA event was first noticed around 8;300' MSL and we climbed as high as 8;700' MSL before we got the aircraft in a descent. The pilot flying started leveling off from the descent because of mountainous terrain. At this point we got a second TCAS RA 'descend; descend' which would have definitely given us a GPWS alert. The pilot flying started a climb; it was our only option because of the rising terrain. Shortly after this; we got the aural message; 'clear of conflict.' During this event we were on the LINDZ9.JNC departure. We flew a heading of 273 degrees to intercept the IPKN northwest course to LINDZ. After we were handed off to center; we were advised of a possible pilot deviation and were given a telephone number to call. We made the call after landing at ZZZ and passengers had departed.Tower put us (the departing aircraft) too close to the arriving aircraft. There needs to be more separation between arriving and departing aircraft.
First Officer reported they failed to comply with two RAs during takeoff so as to avoid flying toward terrain and a possible GPWS warning.