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I am currently watching it right now and I was wondering, when they beamed Kirk and Sulu back up from falling onto the Vulcan planet, wouldn't they still have died? Since the speed they were falling before they were beamed? Also, wouldn't the gravitational pull from the singularity (Black Hole) be too strong for Spock to walk on the planet, let alone run?

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The transporter does not conserve the momentum of the transported, so the speed they were going at is irrelevant.

  • Except that when they land, they land with a thump. So clearly some momentum was preserved. – Valorum Nov 3 '16 at 12:38
  • Here is the (timestamped) relevant part of the scene. The "thump" is not due to any conserved momentum (they would likely be injured or killed if that were the case), and is instead a result of gravity on the ship pulling them down, normally. – Ghoti and Chips Nov 3 '16 at 12:43
  • It's been accepted as the answer (because it's correct), but go ahead and downvote it (you probably already have) seeing as you disagree. – Ghoti and Chips Nov 3 '16 at 12:48
  • I've downvoted for a couple of reasons. First, I don't agree with the premise (as I've mentioned above) and secondly, it's a link-only answer. If the other question gets deleted or the URL changes, your answer becomes worthless. – Valorum Nov 3 '16 at 14:54
  • Your disagreement with the premise is completely false, and has already been refuted, without an appropriate counter-argument. The "link-only" answer is completely acceptable reason for downvoting my answer, I did not know about this particular detail, thanks for the heads up. – Ghoti and Chips Nov 3 '16 at 14:59
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The relevant part in the script is here

TIGHT ON CHEKOV as he struggles to lock onto them -- BEEP!

CHEKOV: Compensating gravitational pull and...

GOTCHA!

He HITS A BUTTON and -- 140 EXT. VULCAN SURFACE

5 FEET BEFORE THEY HIT THE GROUND, KIRK AND SULU DEMATERIALIZE!

INT. ENTERPRISE - TRANSPORTER BAY

AND REMATERIALIZE, SLAMMING DOWN ON THE TRANSPORTER PADS, HARD AND PAINFUL, BUT SAFE! Transporter engineers GAPE in utter amazement and relief -- Chekov, sweating, laughs. Kirk and Sulu get their bearings, peeling themselves up, at stunned whispers

So there you go. He compensated for it, presumably in much the same way that the transporter makes allowances for the ship moving at a different speed from the planet below.

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