Originally Posted by

**Kevlar** This is about dropping a spherical object from 6m high and creating and solving a mathematical model that includes drag.

What i've done so far is.

Got that the force of drag is this

$\displaystyle \mathbf{F}_d= -{1 \over 2} \rho v^2 A C_d \mathbf{\hat v}$

Drawn a free body diagram showin gravity acting downwards[+ve] and drag opposing this[-ve]

Then using F=ma

$\displaystyle mg -{1 \over 2} \rho v^2 A C_d=ma$

(ignored the vector as im working in 1D [V hat])

Then i changed $\displaystyle -{1 \over 2} \rho v^2 A C_d$ by removing $\displaystyle v^2$ to create the constant $\displaystyle k=\frac{1}{2}\rho A C_d$

To get

$\displaystyle mg-k v^2=ma$

then using $\displaystyle a=\frac{dv}{dt}$

i get $\displaystyle mg-k v^2=m\frac{dv}{dt}$

now i'm trying to rearrange this to get my differential eqn this is where i get stuck

from the above im doing this

$\displaystyle dt(mg-k v^2)=m{dv}$

$\displaystyle dt=\frac{m}{mg-k v^2}dv$

now what do i do?