THE FLC OF A BE02 MISJUDGED ACFT PERFORMANCE AND SPACING WHEN THEY DEPARTED BEHIND A C150. THEY OVERTOOK THE ACFT SHORTLY AFTER TKOF AND PASSED OVERHEAD. THE INSTRUCTOR IN THE C150 RPTED THE INCIDENT TO THE AIRLINE.

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MY STUDENT AND I WERE JUST COMPLETING THE RUN-UP OF OUR CESSNA 150 WHEN I TOOK NOTE OF THE BE02 DEPARTING THE TERMINAL AREA. THEY ANNOUNCED THEMSELVES TO THE LCL TFC THAT THEY WERE TAXIING TO RWY 1. THIS IS THE SAME RWY THAT MY STUDENT AND I WERE READYING TO DEPART AND REMAIN IN THE TFC PATTERN TO PRACTICE TKOFS AND LNDGS. WE WERE FINISHING OUR RUN-UP ON TXWY F WHICH INTERSECTS RWY 1 WHEN THE BE02 TAXIED S TO TXWY G AT THE END OF THE RWY. MY STUDENT ANNOUNCED OVER THE LCL CTAF THAT WE WERE DEPARTING RWY 1. AT THE SAME TIME I NOTED THAT THE BE02 WAS PULLING UP TO THE HOLD SHORT LINES ON TXWY G. WITH THE ARRESTOR CABLE JUST N OF TXWY F; MY STUDENT DECIDED TO TAXI ACROSS THE CABLE BEFORE APPLYING FULL THROTTLE FOR OUR TKOF ROLL. AS WE REACHED THE CABLE AND WERE TAXIING OVER IT; THE BE02 PLT ANNOUNCED THAT THEY WOULD TAXI INTO POS AND HOLD. I QUICKLY EXPLAINED TO MY STUDENT THAT HE SHOULD EXPEDITE HIS DEP SO THAT WE WOULD NOT HOLD THE 1900 UP TOO LONG. MY STUDENT APPLIED FULL THROTTLE AND WE STARTED OUR CLBOUT. JUST AS WE STARTED CLBING; MY DOOR CAME AJAR. I IGNORED IT UNTIL MY STUDENT HAD ESTABLISHED HIS CLB SPD OF 70 MPH. BY THIS TIME WE WERE AT ABOUT 300 FT AGL AND JUST N OF RWYS 7 AND 25. I LOOKED OVER TO CLOSE MY DOOR; AS I DID THIS I COULD NOT HELP BUT NOTICE OUR SHADOW ON THE GND JUST E OF RWY 1. THIS DID NOT SURPRISE ME. WHAT DID SURPRISE ME WAS THE SECOND SHADOW WHICH WAS QUICKLY OVERTAKING OURS. I QUICKLY REALIZED WHAT WAS HAPPENING AND TOOK CTL FROM MY STUDENT AND LEVELED THE AIRPLANE. THE BE02 HAD APPARENTLY DECIDED TO DEPART; EVEN THOUGH WE WERE STILL ON OUR UPWIND. THE SHADOW OVERTAKING OURS; I DETERMINED WAS THE BE02 CLBING OUT OVER US. THEY GAVE NO ANNOUNCEMENT OF THEIR DEP OVER CTAF. I LOOKED AROUND TRYING TO DETERMINE THE LOCATION OF THE ACFT BUT COULD NOT FIND IT. I EVEN LOOKED BACK TOWARD THE RWY TO ACTUALLY CONFIRM THAT THE 1900 HAD DEPARTED. IT HAD. WHAT OCCURRED HERE WAS AN OBVIOUS LACK OF COM AND JUDGEMENT ON THE PART OF THE BE02 PLT. EVEN THOUGH HE WAS ABLE TO CLB ABOVE OUR FLT PATH IN ORDER TO AVOID US; DID HE ACTUALLY THINK OF WHAT EFFECT THE WAKE TURB OF HIS ACFT COULD DO TO A LIGHT PLANE LIKE A C150? PERHAPS HE MISJUDGED THE CLBOUT SPD OF OUR AIRPLANE OR MAYBE HE FORGOT ABOUT US COMPLETELY. SUPPLEMENTAL INFO FROM ACN 327191: DEPARTING RWY 1 AT APN FROM THRESHOLD; CALLED POS AND HOLD. THERE WAS DEPARTING TFC FROM AN INTXN 1500 FT UPFIELD. WE ACCOMPLISHED RWY CHKLIST WHILE TAXIING INTO POS WHILE TFC WAS ON THE ROLL. ADDED PWR AND HELD BRAKES WHILE WAITING FOR TFC TO DEPART. WHEN WE THOUGHT THERE WAS SUFFICIENT ROOM WE RELEASED BRAKES AND BEGAN TKOF ROLL. AT ABOUT V1 IT BECAME APPARENT THAT WE WERE RAPIDLY GAINING ON THE CESSNA; WE DECIDED TO CONTINUE ROLL AND MAKE A QUICK TURN TO AVOID GETTING ANY CLOSER. MAINTAINED VISUAL SEPARATION THE WHOLE TIME AND DEPARTED PATTERN. WE ESTIMATED AT LEAST 3000 FT HORIZ SEPARATION DURING ENTIRE INCIDENT. PLT LATER COMPLAINED TO OUR COMPANY OPS. WE MISJUDGED THE SPD DIFFERENTIAL BTWN THE 2 ACFT. CONTRIBUTING FACTOR IS THAT WE OFTEN DEPART BEHIND JET ACFT AT HUBS AND NEVER HAVE A PROB BECAUSE ATC PROVIDES SEPARATION. WE'LL GIVE IT LOTS OF ROOM NEXT TIME.