Free falling particle with air resistance

[carlosbgois]

Homework Statement

A particle is release from rest (y=0) and falls under the influence of gravity and air resistance. Find the relationship between v and the distance of falling y when the air resistance is equal to (a) αv and (b) βv²

The Attempt at a Solution

Setting the origin at the point from where the particle is released, with y pointing downwards, we have, from F=ma, that dv/dt=g-αv, hence ∫dv=∫(g-αv)dt, so, as vdt=dy, v=gt-αy.

Is it right so far? How do I eliminate the time depence? The solution manual has a very different approach that I did not understand, so it may be possible that my attempt won't get me to the answer. Thanks

 

[voko]

How can you represent dt in terms of dy and v?

 

[LawrenceC]

You indicate in the problem statement that air resistance (force) is alpha*v. Then you subtract it from g (gravity) which has different units and set it equal to acceleration. Your units do not jive.