CARJ WITH ZDC EXPERIENCED TCASII RA LEVEL AT FL290 WITH CLBING MD80 RESTR TO FL280.

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DURING CRUISE FLT AT FL290 WE RECEIVED A FREQ CHANGE TO ZDC. I WAS THE PNF AND FO WAS THE PF. I CHKED ON WITH CTR AND SHORTLY THEREAFTER WE RECEIVED A TA 'TFC; TFC' AURAL ALERT. WE SAW THE TFC ON THE TCASII SYS. IT WAS AT OUR 1 O'CLOCK POS AND 1500 FT BELOW US. HE WAS CLBING BUT I DO NOT KNOW AT WHAT RATE. WE BEGAN TO LOOK FOR TFC VISUALLY. AS WE WERE LOOKING; WE RECEIVED AN RA; 'CLB; CLB' AURAL WARNING. FO DISCONNECTED THE AUTOPLT AND BEGAN A CLB AS INSTRUCTED BY THE TCASII SYS. AS THE AIRPLANE BEGAN THE CLB; I CALLED FOR THE CTLS AND CONTINUED THE CLB AT A GREATER RATE. WE RECEIVED THE 'CLR OF CONFLICT' AURAL AT FL300. I XFERRED THE CTLS BACK TO THE FO. I THEN CALLED ATC TO NOTIFY THEM OF THE RA. THEY RECLRED US BACK TO FL290. I THEN CALLED THE FLT ATTENDANT TO LET HER KNOW ABOUT THE RA AND TO CHK THAT EVERYONE WAS OK. ONE OF THE NON-REVENUE PLTS ANSWERED THE INTERPHONE AND NOTIFIED ME THAT THE FLT ATTENDANT HAD INJURED HER ANKLE. THEY HELPED HER TO A SEAT AND PLACED ICE ON HER ANKLE. I CALLED DISPATCH ON COMRDO AND INFORMED THEM OF THE SIT AND THAT THERE MAY BE A POTENTIAL DELAY WITH OUR FLT TO RDU. I TOLD THE DISPATCHER THAT WE WOULD NEED A PARAMEDIC TO MEET US AT THE AIRPLANE IN JFK TO ASSESS FLT ATTENDANT'S INJURY. HE OFFERED TO MAKE THOSE ARRANGEMENTS. AFTER WE LANDED IN JFK THE PARAMEDICS TOOK FLT ATTENDANTS TO THE MEDICAL FACILITY. I THEN CALLED SCHEDULING TO INFORM THEM OF THE SIT. I CALLED THE CHIEF PLT'S OFFICE TO INFORM THEM OF THE SIT AS WELL. SUPPLEMENTAL INFO FROM ACN 627121: MD83 WAS CLBING TO FL280. THERE WAS LEVEL TFC AT FL290. THE CRJ AT FL290 RECEIVED A TCASII ALERT AND RESPONDED. I WAS INFORMED THAT THE FLT ATTENDANT WAS INJURED DURING THE TCASII ALERT. SUPPLEMENTAL INFO FROM ACN 625699: WE RECEIVED AN AUDIBLE TA ALERT FROM THE TCASII. I LOOKED AT THE MFD AND NOTICED THAT THERE WAS AN ACFT AT OUR 12-1 O'CLOCK POS. IT WAS ABOUT 2000 FT BELOW US AND CLBING AT A RATE OF APPROX 500 FPM. AT ABOUT 1400 FT BELOW US; I SPOTTED THE OTHER ACFT; AN MD83. AT THAT TIME; I ANNOUNCED 'TFC IN SIGHT' AND POINTED IN THE DIRECTION OF THE MD83 TO AID THE CAPT.