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

The velocity v(t) of a skydiver falling to the ground is governed by

m(dv/dt)=mg-kv^{2},

where m is the skydiver's mass, g is the acceleration due to gravity, k > 0 is the drag coefficient, and v(t)≥0.

(a) Solve this equation for v(t) with the initial condition v(0).

2. Relevant equations

3. The attempt at a solution

Divide m throughout

==> dv/dt = g - (k/m)v^{2}

Factor out a k/m

dv/dt = k/m (mg/k - v^{2})

Separate

dv / (mg/k - v^{2}) = (k/m)dt

Now I have it in the form ∫ dx/(a^{2}-x^{2}) = (1/2a)ln[(a+x)/(a-x)], with a = √(mg/k) and x=v, obviously.

==> [1/√(mg/k)] ln[ (√(mg/k) + v) / (√(mg/k) - v)] = (k/m)t + C

.............. and this all seems far too complicated.

Suggestions, please.

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# Homework Help: Really Messy Diffy Q

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