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resistance, so the equation is z'' = -gR^2 / (z + R)^2 . Find the relation between v = z' and z and use this model, and the relation that you have

found, to obtain a numerical estimate for the escape speed on the surface of the Earth.

What I've done so far is transformed z'' to vz' using the chain rule.

Next vz' = f(z)

=> 1/2*v^2 = int( f(z)dz + C )

now solve v(z) = dz/dt

=> int (dt) = int(1/v(z)dz)

So I got (gR^2)/(z+R) = (v^2)/2

(2gR^2)/(z+R) = v^2

This is where I got and I don't know where to go next, I don't even know if it's right? Could someone attempt this for me please? Thanks