Let their velocities at 20cm a part be v. Then \\\\( \\Delta KE_{Total} = 2[\\dfrac{Me}{2}v^{2}-\\dfrac{m}{2}(0)^{2}] = Mev^{2} \\\\) Potential energy 10 cm (U Initial ) \\\\( = \\dfrac{-1ke^{2}}{\\dfrac{10}{100}} = 10ke^{2} \\\\)Potential Energy 20 cm (U final ) \\\\( = \\dfrac{ke^{2}}{20/100} = 5ke^{2} \\\\)\\\\( \\Delta U_{Total} = U_{final }-U_{initial} \\\\)\\\\( = 5ke^{2}-10ke^{2} = -5ke^{2} \\\\)As electrostatics force is conservative, \\\\( \\Delta KE _{Total}+\\Delta PE_{Total} = 0 \\\\)\\\\( \\Rightarrow mev^{2}-5ke^{2} = 0 \\\\)\\\\( \\Rightarrow v = \\sqrt{\\dfrac{5ke^{2}}{me}} = 35.58m/s \\\\)