Please! How do you find Terminal Velocity?

Question

jamesj · Answer

You have to model air resistance obviously.  Resistance in general is measured by terms of velocity.  There are two types of terms:
$$ k_1v + k_2v^2 $$
The term proportional to $ v $ is from viscosity of the fluid in which the particle is moving.  The term proportional to $ v^2 $ is due the the pressure of the fluid through which the particle is moving.

In air, it's only the second term we're interested in.  Hence the equation of motion for an object falling through the air near the earth is
$$ \frac{d^2y}{dt^2} = -mg + k\frac{dy}{dt} $$
where y is the vertical distance and of course $ dy/dt = v $.

So that's the general set up to solve the question.

You now need to solve that differential equation and have knowledge of the constant k for air.

jamesj · Answer

You might find this lecture interesting if you're interested in this topic: http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-12/

anonymous · Answer

THANK YOU! but my math teacher asked us for this and we were all confused. But thank you

jamesj · Answer

**correction: the DE should have an m at the front
F = ma, and the net force on the object is
$$ F_{gravity} + F_{resistence} $$
hence
$$ ma = -mg + kv $$
i.e.,
$$ my'' = -mg + ky' $$