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So basically, I'm writing a scene where my main character is standing on a very tall pillar in the middle of nowhere with his master. He learns the basics of this magic, but he doesn't have the luxury to take too long to master it, so his master pushes him off the pillar and he has 6 minutes to master this magic, and figure out a way to use his magic type to avoid falling to his death.

My question is, how high must the pillar be for it to take him 6 minutes to hit the ground if he was pushed at the very top?

This fictional world has the same gravity as earth

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    $\begingroup$ Keep in mind that humans will fall at different rates based on body weight and how they arrange their limbs as they fall. As such, there's not height at which a person will take EXACTLY 6 minutes to fall. The way you phrased the question, it sounds like you want this to be some kind of countdown, but with the number of unknowns, even if you calculate the right height on average, he could hit the ground tens of seconds before or after 6 minutes. $\endgroup$ Jun 28, 2020 at 0:38
  • $\begingroup$ @GiladM, I thought objects fell at the same speed regardless of weight or mass? $\endgroup$
    – Galactic
    Jun 28, 2020 at 6:36
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    $\begingroup$ @Galactic: All objects fall at the same speed in a vacuum. Earth's atmosphere is not a vacuum. When objects fall in a viscuous fluid, such as air, they accelerate up to the point where the drag (= the resistance of the fluid against the motion of the object) equals their weight; from that point on their speed remains constant. This final speed is called terminal velocity and depends on the weight and shape of the object and on the viscosity of the fluid. $\endgroup$
    – AlexP
    Jun 28, 2020 at 7:02
  • $\begingroup$ Neither the down vote nor the close votes are mine - but I understand why they're there. This is just a math question and has little to nothing to do with building the rules or systems of a world. In fact, it could almost be VTCd as too story based because everything from what the dude was wearing to his shape and height to his hair and even how hard the master pushed him contribute to the answer. $\endgroup$
    – JBH
    Jun 28, 2020 at 16:25

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In a zeroth order approximation, about 19 km or 12 miles or 62,000 feet. That's about twice the height of Mount Everest.

Justication: The terminal velocity of a human falling in Earth's atmosphere is about 54 m/s.

If the character has some suitable clothing, the terminal velocity can be smaller, and thus he can jump from a lower altitude and still take 6 minutes to reach the ground.

(In reality, at 19 km altitude the terminal velocity will be much higher; so that 19 km is not enough. But I don't feel like calculating a better approximation.)

(Please note that at such a high altitude the character and his master better have vacuum suits, because otherwise they will suffocate.)

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  • $\begingroup$ I'm not a maths expert, but if I cut the time down to 3 minutes, does that bring the height down to 31,000 feet? If yes, do my characters still need vacuum suits? $\endgroup$
    – Nass King
    Jun 28, 2020 at 0:00
  • $\begingroup$ The other variant of my "comment" question is, at the limit of altitude, how high would the pillar have to be for them not to need vacuum suits, and how many minutes would it take him to fall from that height?? $\endgroup$
    – Nass King
    Jun 28, 2020 at 0:02
  • $\begingroup$ At what altitude people need supplementary oxygen depends on the person in question; generally, some people need supplementary oxygen at 4,000 meters, some do fine at 5,000 meters, and a few try to scale the Everest without oxygen. Yes, most of the fall is at terminal velocity (it takes only about 6 or 7 seconds to reach it). $\endgroup$
    – AlexP
    Jun 28, 2020 at 0:12
  • $\begingroup$ Then I think I'll go with the direction of making this particular area a magical dimension where you can still find oxygen/air at 62,000 feet above. I suppose this works, right? $\endgroup$
    – Nass King
    Jun 28, 2020 at 0:27
  • $\begingroup$ @AlexP It also depends on what tasks the person has to perform. Oxygen is not needed for passengers taking off from El Alto, SLLP. It is required for pilots. $\endgroup$ Jun 28, 2020 at 0:31

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