1. The problem statement, all variables and given/known data Consider a particle of mass m whose motion starts from rest in a constant gravitational field. If a resisting force proportion to the square of the velocity (i.e. kmv^2) is encounterd, show that the distance s the particle falls in accelerating from v0 to v1 is given by s=(1/2k)*ln[(g-kv0^2)/(g-kv1^2)] 2. Relevant equations 3. The attempt at a solution I am continually frustrated by these types of problems because I struggle with coming up with a DE that I can solve. my''= km(y')^2 -mg y''= k(y')^2 - g so I have a non linear equation I wanted to make a substitution u = y' so that u'=ku^2 - g, but this doesn't help at all. Can someone please point me in the right direction? Thanks.