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Is acceleration law

$a = \Delta v/\Delta t$

applicable on somebody who is falling from an air plane? Does the acceleration increase when some body is at some altitude and does his speed increases by $9.81 m/s$ every second (because of the gravity of the average earth) ?

JDługosz
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Maroxtn
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  • In this special case yes, because $a$ is constant, so average rates of change $\Delta v/\Delta t$ and instantaneous ones $\frac{\mathrm{d},v}{\mathrm{d},t}$ are equal. – Selene Routley Jan 29 '15 at 21:31
  • @WetSavannaAnimalakaRodVance the gravitational force is constant, but the acceleration most definitely is not: it falls to zero pretty quick due to wind resistance, when terminal velocity is attained. – Level River St Jan 29 '15 at 21:34
  • @steveverrill Maybe you could make that into an answer, however it is a little unclear whether the OP is asking a "homework" question with assumed constant acceleration or whether they need to take air resistance into account. Looks like two people have beaten you to it, though! – Selene Routley Jan 29 '15 at 21:37

2 Answers2

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If I understand what you asked, yes that is the situation for which acceleration due to gravity is applied.

However, there is a terminal velocity due to air resistance, and the Acceleration and resistance will reach equilibrium. The wikipedia page discusses skydiving first, and that is what the activity of purposefully jumping out of a plane is called.

tom
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JDługosz
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  • nice answer +1 - edited some spellings – tom Jan 29 '15 at 21:37
  • Thanks, @tom. The tablet makes simple edits challenging! – JDługosz Jan 29 '15 at 21:43
  • So this means that the speed of the sky diver is limited ? – Maroxtn Jan 29 '15 at 21:48
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    Yes, between 100 and 200 miles per hour depending on whether he's wearing baggy clothes and spread horizontally, or wearing sleek clothes and head-down vertical. Of course a parachute is simply a more extreme example of the same effect. – JDługosz Jan 30 '15 at 15:06
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Yes speed will increase $9.8$ m/s every second provided that there is no other force acting as resistance to the fall.

In reality air resistance depends on speed and the faster someone falls the more the resistance of the air around them. Eventually any object falling through the atmosphere will reach 'terminal velocity' the speed at which the force downwards of gravity is balanced exactly by a force upwards of wind resistance.

One final point is that at high altitude the acceleration due to gravity will be slightly less as the acceleration due to gravity depends on the distance from the centre of the earth. - but then the air is less dense so the air resistance will be lower and the terminal veocity will be higher.

tom
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  • So this means that the speed of the sky diver is limited ? – Maroxtn Jan 29 '15 at 21:43
  • @Maroxtn - I've read that a sky diver, by making his body into a "bullet" aimed straight down, can achieve around 200-250mph. When falling in the familiar "spread eagle" form, with arms and legs outstretched and the body fairly horizontal, the terminal velocity is somewhere near 60mph, and much less if the skydiver is wearing a "wingsuit". – Hot Licks Jan 29 '15 at 21:49
  • @Maroxtn - Note that those values are from memory, and mine is not known to be highly reliable. But they should be in the ballpark, and it's kind of a "soft" question anyway, since a lot depends on conditions. – Hot Licks Jan 29 '15 at 22:03
  • @Maroxtn - skydiver terminal velocity about 120 mph from http://hypertextbook.com/facts/JianHuang.shtml – tom Jan 29 '15 at 22:45
  • With or without parachute opened ? @tom – Maroxtn Jan 30 '15 at 10:19
  • @Maroxtn - 120 mph without parachute opened. – tom Jan 30 '15 at 23:13