[shockwavemikey65 (OP)]

I need to know the terminal velocity of a 290lb 6'6" person, as well as how long it will take this person to reach terminal velocity.

I also need to know how to incorporate that into a project in my math class. I need to use an exponential growth in the rate of descent, as well as how to factor in acceleration due to the force of gravity.
Considering this person will do a half flip off of a rooftop and probably land on their back on a pole vault mat from a building about 2-3 levels.


Can any one please help?
The project is due in a week!

[DoctorBeaver]

Welcome to TNS.

This is what the Guinness Book of Records has to say:

It is estimated that the human body reaches 99% of its low-level terminal velocity after falling 573m 1880ft which takes 13-14 sec. This is 117-125mph at normal atmospheric pressure and in a random posture.

I regret that I cannot elucidate further; but we have some very good mathematical minds on this site who will probably help you out.

 

[syhprum]

Assuming a drop of 10 meters air Resistance will have very little effect hence your velocity when you reach the mat will be determined solely by your acceleration 'G'.

Acceleration  G = 9.81 M/S^2

Distance      D = (G*T^2)/2

Time          T = (2*D/G)^0.5

Velocity      V = G*T = 14 Meters/sec

Good luck with the back flip!

[DoctorBeaver]

14mps? You'd better get 2 pole vault mats!  []

[daveshorts]

Until the person is going very close to their terminal velocity the increase in their speed is not going to look anything like an exponential of any form. For those distances of fall you could make a pretty good approximation that the air resistance is zero. If you wanted to justify this, air resistance will tend to go about as the square of your speed.

So  F_air = k v²

at terminal velocity

F_air = F_gravity

so

k v² = mg

from this and the terminal velocity of a person you can work out k and then work out an approximation for the maximum force applied by air resistance by finding the maximum velocity in your situation without air resistance and then sub it into the above equation. If it is really insignificant a physicist would ignore it.

If you want to solve for the speed including air resistance you are going to have to do some fun calculus...

[syhprum]

I think professional stunt men use a large stack of (restrained) air filled cardboard boxes to fall onto

[DoctorBeaver]

I think professional stunt men use a large stack of (restrained) air filled cardboard boxes to fall onto

Yes

[lyner]

Less invasive experiments can give you very interesting results. If you drop a pingpong ball from about 20m in still air, the effects of air viscosity can be  seen; it accelerates measurably less at the bottom than at the top (metres per second squared). It is not at terminal velocity but it is starting to show the effects.
AS far as a dropping person is concerned, health and safety really militates against this experiment.
As a matter of fact, the rate of increase of velocity is NOT exponential - it is proportional to the square of the time (equations of motion under uniform acceleration etc). If this is supposed to be a Maths project, you should get the Maths right - n'est pas?
Possibly, you don't mean terminal velocity. . .  either.
According to Galileo, the mass of the falling body should not have any effect (until you reach speeds where the drag from the air is relevant).

[shockwavemikey65 (OP)]

Less invasive experiments can give you very interesting results. If you drop a pingpong ball from about 20m in still air, the effects of air viscosity can be  seen; it accelerates measurably less at the bottom than at the top (metres per second squared). It is not at terminal velocity but it is starting to show the effects.
AS far as a dropping person is concerned, health and safety really militates against this experiment.
As a matter of fact, the rate of increase of velocity is NOT exponential - it is proportional to the square of the time (equations of motion under uniform acceleration etc). If this is supposed to be a Maths project, you should get the Maths right - n'est pas?
Possibly, you don't mean terminal velocity. . .  either.
According to Galileo, the mass of the falling body should not have any effect (until you reach speeds where the drag from the air is relevant).

OK. well in that case how would I apply the flip from the roof onto the mat to show a graph of this stunt? I need to show all of the forces that act on the stunt from how fast he was running on the roof until about how much force is exerted when the person hits the mat.
By the way the teacher gave us 2 weeks so all help is greatly appreciated!

[syhprum]

These are very simple calculations that only require the application of the formulae that I have previously quoted !

[shockwavemikey65 (OP)]

These are very simple calculations that only require the application of the formulae that I have previously quoted !

Thanks a lot!