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captainjack2000
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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