Question of Physics?

Question

At what height would a 200 lbs. person have to fall from in order to reach terminal velocity?

Answer 1

The terminal velocity is a result of the force of gravity and the force of the air drag canceling each other out. The terminal velocity depends on the weight of the object, its cross-sectional area, aerodynamic properties (drag) and the density of the air (or in general fluid) it falling through.
V= (2mg/pAD)^1/2=SQRT(2mg/pAD)
Where
V is the terminal velocity, (in meters/second)
m is the mass of the falling object, (in kg)
g is gravitational acceleration, (9.81 m/s^2)
D is the drag coefficient,
p is the density of the fluid the object is falling through (air~1.29kg/m^3)
A is the object's cross-sectional area.


So to answer you question you also have to know what the person was wearing, has that person maintained horizontal or vertical position during the flight and so on.

Computing particular objects cross-sectional area is usually straight forward however the drag coefficient is best determined experimentally. No, I’m not saying that we would have to drop your 200 lb person to determine his/her drag coefficient instead we can ask that person to ride a bicycle. To estimate the drag force one has to compute by how much the rider sitting straight and with legs extended downward will drop its velocity from v2 to v1 within a particular time interval t. The negative acceleration (or sometimes called deceleration) a will be approximately a=(v2-v1)/t . Since we know the mass of the rider and bicycle we can estimate the air drag force.
And using the equation F=(m1+m2)a=(DpAv^2 where v=(v2-v1)/2
So
D=4((m1+m2) (v2-v1)/(tpA (v2-v1)^2)= 4((m1+m2) /(tpA (v2-v1))

Answer 2

This website will give you everything you need to figure it out yourself...

http://www.grc.nasa.gov/WWW/K-12/airplane/termv.html