Answer
$v=0.95c$
Work Step by Step
$p_1=p_2$
$p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2} }}$
$\frac{(6.68\times10^{-27}kg)(0.6c)}{\sqrt{1-\frac{0.36c^2}{c^2} }}=\frac{(1.67\times10^{-27}kg)v}{\sqrt{1-\frac{v^2}{c^2} }}$
$3c=\frac{v}{\sqrt{1-\frac{v^2}{c^2} }}$
$9c^2-9v^2=v^2$
$9c^2=10v^2$
$v=\sqrt{0.9}c=0.95c$