Ask A Scientist© Physics Archive

 
 
>
> >  name       Mike
> >  status     other
> >  age        30s
>
> >  Question - I'm a Police Officer in Ada, Oklahoma. Last week we had a
> > suicide, where the Individual jumped to his death. He weighed
> > approximately 160 pounds and fell 51 feet to his death. During the
> > investigation, it was pondered on how long he was in the air before he
> > landed. It appears that he jumped out from where he was standing 3-5
> > feet. Can you please help? Doesn't an object reach terminal velocity
> > within 32 feet of falling? One Officer believes it took approx 1.5
> > seconds, and myself and the medical examiner where thinking it took
> > approx 2 to 2.5 seconds.
> >
> >thank you
> >Mike Baker
>
>Answer:
>Eric Tolman
>Computer Scientist
>
>Terminal velocity makes the problem a lot more tricky, but fortunately, this
>doesn't look like terminal velocity had much of an effect in this case.
>
>For a typical person, terminal speed is 60 m/s or approximately 135 miles
>per hour. A person has to fall over 400 yards before you really need to
>start taking this into account.
>
>The 32 feet you remember is the acceleration to gravity. A falling object
>increases its velocity by 32 feet per second per second it falls.
>
>Also, the fact that he jumped out doesn't really affect the equations. If
>he jumped up or down that would change things slightly, but probably not
>enough to change the answer by more than a very small fraction of a second.
>
>First we convert feet to meters:
>
>51 feet = 51f/3.28f/m = 15.55 m.
>
>So, from physics we can use the formula for constant acceleration:
>
>x - x0 = v0 * t + 1/2 a*t*t
>
>51/3.28 = 0 + 1/2 * 9.8 * t * t
>
>15.55 = 4.75 * t * t
>
>3.273 = t*t
>
>t = sqrt(3.273)
>
>
>Time it took then is: 1.81 seconds.
>
>
>Thanks,
>Eric Tolman
=========================================================
>By my calculation, it would have taken about 1.8 seconds. t =
>sqrt(2x/a), where 'x' is the distance in meters and 'a' is 9.8 m/s/s,
>the acceleration of gravity.
>
>When the guy landed, he would have been moving at around 17
>meters/second or 38 mph. I doubt this is close to terminal velocity
>for a body. I've heard that skydivers routinely get over 100 mph.
>If so, then it's ok to ignore air resistance in this calculation.
>
>Tim Mooney

=========================================================

>If one simply assumes that the object fell 51 feet, without air resistance
>and zero initial velocity, at least in the vertical direction, then the
>object would have been in the air for 1.78 seconds. Distance= Acceleration
>due to gravity x time x time/2
>51=32x t squared/2 or the time= 1.78 seconds.
>The other factor such as initial velocity in the vertical direction would
>reduce the time in the air. Achieving terminal velocity, would also increase
>the time in the air. Unless the poor chap fell with his body parallel to the
>ground, I doubt that terminal velocity played a role in this scenario.
Dr. Myron
=========================================================

>First of all, science aside, my condolences to the victim and his family.
>Someone takes his own life only when something, somewhere, has gone terribly
>wrong.
>
>Back to science. You can probably ignore the effects of wind resistance for
>a human body falling 51 feet. To reach terminal velocity, the wind drag
>force must equal the weight of the falling body. You have to be going
>pretty fast for this to happen. Without wind resistance, the speed of a
>falling object increases by 32 feet per second each second. (This is
>probably where you heard the "32 feet" number.) It takes a little calculus
>to figure out how fast an object will be going after falling for 51 feet,
>and how long it takes to fall that distance. Assuming that it starts from a
>dead stop, the formulas are:
>
>velocity = v = sqrt(2gh)
>time = t = sqrt(2h/g)
>
>where h is the height (distance the object falls) and g is the gravitational
>acceleration, (32 feet/sec)/sec. From these formulas, an object would take
>1.8 seconds to fall 51 feet, and would be traveling 57 ft/s (40 mi/h) when
>it gets there.
>
>That doesn't sound very fast, does it? It should put into perspective how
>deadly car crashes can be without all those modern safety features.
>
>Richard E. Barrans Jr., Ph.D.
>Assistant Director
>PG Research Foundation, Darien, Illinois
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