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Deputy principal rural fire officer Jamie Cowan, of the Otago Rural Fire Authority, said the rocket, fired from several hundred metres away, landed in an undeveloped section covered in long grass.
The fire, fanned by a strong breeze, scorched an area about 200m x 200m.
Twenty volunteer firefighters from Arrowtown and Frankton, including Arrowtown’s rural brigade, fought the blaze for almost two hours, using three fire appliances and a water tanker.
Many volunteers wielded hand-held fire beaters.
"Just a good reminder, really, to everybody that we are heading into summer and long, dry grass will burn," Mr Cowan said.
"Costs will be recovered from those responsible."
The teens were co-operative and remorseful, he said, and happy to pay costs — which he estimated would be a few hundred dollars.
He described the fire as reasonably fast-moving. It was contained by nearby driveways and slowed by green grass.
No houses were threatened.
"Lucky it is only October," he said.
"We were lucky the breeze was coming from the south. Had it been going one of the other directions it could easily have pushed it around that Lake Hayes face."