How Is Distance Calculated in Free Fall with Air Resistance?

[bigjuicy]

D=Drag Coefficient
p=Density of air
A=Cross sectional area
v=velocity
a=acceleration
F= force

F air=(DpAv^2)/2
F net=mg-F air
ma=mg-F Air
a=g-(DpAv^2)/2m
k=DpA/2m

so
a=g-kv²
dv/dt=g-kv²
dt=dv/g-kv²

using the online integrator from wolfram we got

t=tanh^-1(sqrt(k)v/sqrt(g))/sqrt(gk)

we want to solve for distance fallen without t or v in the equation

 

[tiny-tim]

welcome to pf!

hi bigjuicy! welcome to pf!

(have a square-root: √ )

t=tanh^-1(sqrt(k)v/sqrt(g))/sqrt(gk)

we want to solve for distance fallen without t or v in the equation

i'm a little confused as to what you're doing …

you have dz/dt (=v) as a function of t, so solve for z the usual way (but how can you solve for z without t, when distance fallen depends on time? )