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Differential equation

1. 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.


2. Homework Equations


3. 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
 

Answers and Replies

Dick
Science Advisor
Homework Helper
26,258
618
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?
 

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