Particle falling in earth's gravity with air resistance.

[kraigandrews]

Homework Statement

A particle falls in Earth's gravity. The force of air resistance is F = −αv v where v is the velocity, v is the speed, and α is a constant. (The direction of the force is opposite to the velocity, and the magnitude of the force is αv2.) If the terminal speed is 20.2 m/s and the mass is 2.6 kg, determine the constant α.

Homework Equations

F=ma=mdv/dt

The Attempt at a Solution

I was hoping somebody could point me in the right direction. I know how to solve a problem with just a resistive force, however, I am not sure where to start when given both the speed and velocity vector in the retarding force. So just any guidance as to where to start would be greatly appreciated.
Thanks.

 

[Uncle_John]

You could solve this by solving the differential equation that way you'll get the x(t) function, and from there you can calculate the constant

or, you could think about the force balance after some time when particle reaches it's final speed

 

[George Jones]

Start with F = ma. What are the expressions for the individual forces that act on the particle? What is the net force F that acts on the particle?

 

[kraigandrews]

Ok, so how would I incorporate the vector v and the speed v into the diff eq?

 

[Uncle_John]

you can divide it into components, and then solve the differential equation for each component, that's harder way than just writing the net force balance for the time when speed reaches it's final speed, but you'll learn more from it;)