C172 CFI AND STUDENT AVOID NMAC WITH GULFSTREAM IV DEPARTING MMU.

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MMU CLRED MY PLANE (C172RG) (WITH PVT PLT ON PRACTICE FLT) TO DEPART RWY 5; MAINTAIN 1300 FT; BEFORE ON COURSE; TURN NW. NO OTHER ACFT COMS WERE HEARD. HOWEVER; MMU TWR; ON OUR TKOF ROLL; ADVISED ANOTHER ACFT THAT THE ACTIVE WAS GOING TO BE CHANGED. AT 1100 FT; WHILE CLBING STRAIGHT-OUT PRIOR TO L TURN; I SAW A GULFSTREAM AT MY IMMEDIATE 11 O'CLOCK POS; ON A R BASE TO FINAL IN A SEVERE SHORT APCH. IT WAS DIFFICULT AT FIRST TO DETERMINE PROPER EVASIVE ACTION; BUT I DETERMINED AN IMMEDIATE L CLBING TURN. THE GULFSTREAM WAS WITHIN 100 YARDS. UPON QUERYING TWR; GULFSTREAM PLT CAME BACK WITH 'IF YOU HAD MODE C ON; WE WOULD HAVE SEEN YOU.' WE HAD PROPER MODE C ON. THE GULFSTREAM NEVER LOOKED. TWR HAD NO COMMENT. THE GULFSTREAM WASN'T ON 118.1 WHEN I DEPARTED; OR AT LEAST I NEVER HEARD HIS COM WITH TWR. THE GULFSTREAM MADE AN INORDINATELY SHORT APCH WITHOUT LOOKING OUTSIDE THE PLANE -- AS IS HIS RESPONSIBILITY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THE INITIAL TWR CLRNC TO CLB TO 1300 FT BEFORE STARTING A TURN WAS UNUSUAL; BUT NO REASON WAS GIVEN. WHILE HE HEARD THE TWR ADVISE SOMEONE THAT A CHANGE IN ACTIVE RWY WAS FORTHCOMING; HE NEVER HEARD THE GULFSTREAM IV ON THE FREQ. THE RPTR TOOK CTL OF THE ACFT TO MAKE THE EVASIVE MANEUVER WHEN THE TFC WAS SIGHTED. HE ALSO INDICATED THAT THE GULFSTREAM IV FLC DID NOT HAVE HIS ACFT N SIGHT UNTIL THE LAST MIN DUE TO THEIR COMMENT REGARDING HAVING THE MODE C ON. THE RPTR IS QUITE FAMILIAR WITH THE OP AT MMU AND STATED THAT THE TFC PATTERN ALT FOR JET TFC IS 1500 FT; SUGGESTING THAT THE GULFSTREAM IV SHOULD HAVE BEEN ABOVE HIM HAD THEY BEEN FLYING A NORMAL PATTERN.