# Classical Mech - Newtons 2nd. Quad Air Resistance

1. Sep 9, 2014

### MPKU

1. The problem statement, all variables and given/known data

A puck of mass m is kicked up an incline (angle θ) with initial speed vo. Friction is not present, but air resistance has a magnitude of f(v) = cv2. Solve Newtons second law for the pucks velocity as a function of t on the upward journey. How long does the journey last?

2. Relevant equations

3. The attempt at a solution

mv' = -mgsinθ - cv2 v(hat)

dv/dt = -gsinθ -(c/m)v2 v(hat)

dt = -dv/ (gsin θ -(c/m)v2 v(hat) )

I'm not quite sure how to solve this; perhaps I could rewrite to get a known integral of 1/(1 +x^2) dx, but I don't see how.

2. Sep 10, 2014

### haruspex

You can drop the v(hat), since you've reduced it to scalars, all motion being in the one dimension.
Can you do it from there?

3. Sep 10, 2014

### MPKU

I don't think so. Should I just rewrite it as:

dt = -(gsin θ -(c/m)v^2)^-1 dv and integrate?

4. Sep 11, 2014

### haruspex

Yes, except that you just made a sign error.