Solving a Nonlinear ODE for Parachute Area in Free Fall

[francisg3]

Homework Statement

We recently discussed a problem in class involving free fall and parachutes.One of the examples was to solve for the area of a parachute in drag,gravity,air density,mass and the speed at which the object deployed the parachute and the speed it hit the ground out. I'm pretty sure I know how to do the porlbem if I could only get past the first few steps. My guess is that I need to solve the following nonlinear ode:

m (dV/dt) = mg-(1/2)(air density)(drag constant)(area parachute)(V)^2
i replaced the equation with something like this to simplify it:
m (dV/dt) = mg-kV^2 where k is all those constants

now I'm familiar with seperable ode's and this is the form i obtained:
dV/dt = g-(k/m)V^2

from then on i am lost, i think i just need a bit of help onto the next step or two then i should be able to get the problem rolling. Any help or input would be greatly appreciated! Thank you.

 

[tiny-tim]

Welcome to PF!

Hi francisg3! Welcome to PF!

(try using the X² tag just above the Reply box )

dV/dt = g-(k/m)V^2

yes, so dV/(g-(k/m)V²) = dt

 

[HallsofIvy]

And you can use partial fractions to integrate that.