Factual error: Enterprise and Vengeance come out of warp near the moon, 237,000km from Earth. Due to their altercation. They lose power and proceed to fall freely toward Earth. The scene plays as though it takes a matter of a few minutes, too fast to get the situation under control. At that distance, the gravity acceleration from Earth would only be .01 m/sec/sec. This means that they should have had approximately 2.52 days before crashing, especially given their apparent relative stop as per the visible moon.
Star Trek Into Darkness (2013)
Ending / spoiler
Directed by: J.J. Abrams
Starring: Benedict Cumberbatch, Simon Pegg, Chris Pine, Karl Urban, Zoe Saldana, Anton Yelchin, Alice Eve, John Cho, Zachary Quinto
Kirk sacrifices himself by going into the radiation chamber to restart the Enterprise. Khan's ship crashes in San Francisco and Spock chases after him. Bones discovers that Khan's blood has healing properties - Spock knocks out Khan and his blood is used to save Kirk. Khan is put back into cryo sleep with the rest of his men. The Enterprise embarks on a 5 year mission.
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Bones: Jim, you just sat that man down at a high-stakes poker game with no cards and told him to bluff. Now, Sulu's a good man, but he's no captain.
James T. Kirk: For the next two hours, he is. And enough with the metaphors, all right? That's an order.
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Answer: Unless the cold fusion went directly into the volcano, all the way to the source of the pressure.