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Is atmosphere depth important in reaching terminal velocity in terms of slowing down an object. For instance, if a meteor was dropped from height $h_1$, would it hit the ground with the same velocity as if it were dropped from say twice that height? The drag force in the latter scenario would be greater at each point in time in the meteors descent, since it would be entering the atmosphere faster and the drag is proportional to velocity.

Follow-up question:

IF its not important, why is it that when you drop say a cup (a plastic one that floats if left in water) full of water in a bath tub, it creates quite a noise, from the fact it hits the bottom of the bath fast, but if you drop the cup half that height it wont be as loud (it hits the bottom slower), and if you 'drop' the cup in the bath, it floats.

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The important thing is the initial velocity, and that there is enough height to reach the terminal velocity. If the meteor hits the atmosphere at the same velocity, the drag forces on it will be the same no matter what the height is. And if the atmosphere is thick enough so that this drag will make it reach the terminal velocity, then it will continue at this velocity indefinitely towards the ground.

(Actually the force of gravity changes with height, as would air density, but I'm ignoring that.)

For the example of the cup, the difference is that dropping the cup from a greater height means that it reaches the water's surface at greater velocity. The cup doesn't really move through the water at its terminal velocity. If you imagine dropping a solid-cup that sinks in water, on the other hand, and dropping it into a pool, then after a short distance the cup would reach its terminal velocity and will from that point on fall towards the bottom of the pool with this velocity regardless of how far you dropped it.

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  • $\begingroup$ The terminal velocity is dependant on the atmospheres density. $\endgroup$
    – Think
    Jan 31, 2019 at 13:22
  • $\begingroup$ I imagine that if a meteor enters the atmosphere ridiculously fast, it will be like hitting water at high speed, which would slow it down tremendously. Whereas if the same meteor entered the atmosphere slower, the drag on it would not be as great, would this cancel out causing the meteors to effectively be travelling at the same speed almost instantly? $\endgroup$
    – Think
    Jan 31, 2019 at 13:46
  • $\begingroup$ Yes, I ignored atmospheric density; I'd add it to the above disclaimer. The effect of extra-speed would not quite cancel-out as after some time the fast-hitting meteor would reach the slow-hitting meteor's initial speed and only from that time will the dynamics become similar. Both would reach their terminal velocity if the atmosphere is thick enough. $\endgroup$
    – PhysicsTeacher
    Jan 31, 2019 at 14:00
  • $\begingroup$ Ok, so the depth of the atmosphere is important. $\endgroup$
    – Think
    Feb 3, 2019 at 0:30
  • $\begingroup$ the extra force from the extra speed doesn't cancel out with the fact its going faster $\endgroup$
    – Think
    Feb 3, 2019 at 0:31

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