1. N2L/D.E easy but hard???

A parachutist of mass 80kg falls vertically from rest from a stationary helicopter. At a distance xm blow the helicopter her velocity is vms-1. The forces acting on her are her weight and air resitance of magnitude kv^2, where k is a constant. Her terminal velocity is 70ms-1. (i) show that the motion may be modelled by the D.E

vdv/dx = 9.8 -0.002v^2
This makes no sense, where does the v come from. n2l staes mass x acceleration! I am missing someting vital pls help!

2. Originally Posted by i_zz_y_ill
A parachutist of mass 80kg falls vertically from rest from a stationary helicopter. At a distance xm blow the helicopter her velocity is vms-1. The forces acting on her are her weight and air resitance of magnitude kv^2, where k is a constant. Her terminal velocity is 70ms-1. (i) show that the motion may be modelled by the D.E

vdv/dx = 9.8 -0.002v^2
This makes no sense, where does the v come from. n2l staes mass x acceleration! I am missing someting vital pls help!
You might find it helpful to note that
$\displaystyle v \frac{dv}{dx} = a$
in all cases.

(Make sure you understand why this is so.)

-Dan