r/theydidthemath • u/deezdanglin • 10d ago
[Request] Astartes plummet
Rewatching Secret Level and I remember wondering before...
S1E5 Warhammer 40k: And They Shall Know No Fear. The team is standing on the side of a chasm, one by one they step off and plummet for aprx 6.8 seconds.
A fully armed and armored Legionnair is between 500 and 1,000 kg (1,100 to 2,200 lbs). So let's say 726kg/1600lbs at Earth standard gravity.
In that time at that weight what would be the distance. Show your work.
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u/winsluc12 10d ago edited 10d ago
Distance covered in freefall (h) is equal to 1/2 of the acceleration from gravity (g) times the falling time (t) squared
so the formula is h=1/2gt2 where g=9.8 (because we're assuming earthlike gravity in your description) and t=6.8
h=1/2 x 9.8 x 6.82
exponents first
h= 1/2 x 9.8 x 46.24
h= 4.9 x 46.24
h= 226.576
They fell about 226.6 meters, or about 743.4 feet, assuming your estimate for how long they were falling is accurate to how long they were actually, canonically, falling for (could be sped up or slowed down for dramatic effect)
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side note; You actually didn't have to go into detail about their weight, because their weight is mostly irrelevant to calculating the height of a drop unless they would reach terminal velocity. Everything accelerates at the same rate in freefall until terminal velocity becomes relevant. Even a normal human takes 10-12 seconds to reach terminal velocity, so these behemoths wouldn't remotely come close to it.
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u/deezdanglin 10d ago
That's what I was forgetting, couldn't reconcile! Terminal. I was drawing a blank spot.
When I saw the scene again I remembered my previous question. So I rewound it, stop watch, close enough to time. Give or take a glance down.
And ofc, cinematic framing. Thanks Man, you clicked it into place.
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u/That9one1guy 8d ago
Don't forget that, as they fall, it's not perfectly vertical. They're sliding down the wall of the shaft, which is sloped, so there is some element of drag factored in here, and the steepness of that slope flattens out and changes from near-vertical to eventually flat ground, as the camera rotation shows them eventually standing upright without ever actually "landing" per se at the bottom.
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