J3 CUB STUDENT PILOT ON SOLO CROSS COUNTRY; REPORTS PROP STRIKE AFTER ATTEMPTING TO CORRECT AN IMPENDING GROUND LOOP WITH BRAKES.

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I; AS FLT INSTRUCTOR; DISPATCHED MY 39 HR TOTAL TIME STUDENT ON HIS FIRST OVER 25 MI SOLO XCOUNTRY IN A J3 CUB. HIS TOTAL SOLO TIME TO DATE WAS 5.3 HRS. WE HAD FLOWN THE EXACT SAME RTE THE DAY BEFORE. THE WX THIS DAY WAS CAVU WITH WINDS FROM THE NW AT LESS THAN 10 KTS. CONDITIONS WELL WITHIN MY CONSTRAINTS OF 5000 FT; 5 MI; MAX XWIND OF 10 KT. HE HAD DEMONSTRATED 3 POINT AND WHEEL LNDGS ON BOTH GRASS AND HARD SURFACE MANY TIMES BEFORE IN CONDITIONS THAT EXCEEDED MY 10 KT XWIND LIMIT. ALL LOGBOOK ENTRIES WERE CONFIRMED. WE BOTH INDEPENDENTLY CHKED THE WX AND CONFIRMED IT WAS OK FOR THE FLT. I CHKED ALL NAV CALCULATIONS AND FOUND THEM CORRECT. I OBSERVED HIS PREFLT; TAXI OUT; AND DEP. ALL PROPERLY EXECUTED. SOME TIME LATER; HE CALLED ME ON HIS CELL PHONE AND SAID THAT ON ROLLOUT ON THE HARD SURFACE AT ZZZ HE FELT THE CUB 'WAS GOING TO GND LOOP SO HE APPLIED BRAKES CAUSING THE CUB TO NOSE OVER AND STRIKE PROP.' THE DAMAGE CONSISTED OF THE PROP/ENG; COWLING AND HIS PRIDE. IT APPEARS THAT HE MAY HAVE APPLIED BRAKE THAT MAY HAVE BEEN APPROPRIATE FOR A GRASS RWY BUT TOO MUCH BRAKE FOR HARD SURFACE. SUPPLEMENTAL INFO FROM ACN 763468: PIPER J3 CUB BEING FLOWN BY STUDENT PLT. AFTER TOUCHDOWN DURING ROLLOUT; STUDENT PLT EXPERIENCED THE START OF A GND LOOP; ATTEMPT TO CORRECT WITH RUDDER AND BRAKE RESULTED IN NOSE DOWN ATTITUDE STRIKING PROP; STOPPING ENG; AND CONTACTING RWY. TO PREVENT A RECURRENCE; LESS BRAKE APPLICATION ON HARD SURFACE RWY; ESPECIALLY WHEN FLYING SOLO IN J3 CUB.