(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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. Relevant 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

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# Homework Help: Differential equation

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