When will an object with air resistance hit the ground?

[captainjack2000]

Homework Statement

mass m released from a height h falls to the ground under the influence of gravity. It is acted on by air resistance which has the magnitude k times the speed. Show that the mass hits the ground after a time T given by
T=kh/mg + m/k(1-exp(-kT/m))
ii)assume two objects of identical size and shape but differing masses are dropped simultaneously. working in first order of k/m determine whether they hit the ground at the same time or if not the time difference.

Homework Equations

The Attempt at a Solution

Taking downward direction as positive I have the equation of motion
m(dv/dt) = mg-kv
(dv/dt) = g-(k/m)v

integrating from 0 to v(t) and from 0 to T using separable equations I got
(m/k)ln(1+m/(kv(t))) = T
so
v(t) = (1/k) exp (-kT/m)(m+1)

Could someone tell me if this is right and how to go about finding the time of flight?

Thanks

 

[Dick]

You are leaving out too many steps. Those aren't right and you omitted the details of the steps where you are going wrong. For example, whatever happened to 'g'? In a correct answer as t->infinity, v*k should approach m*g, right?