Explanation

(b) Conserving the momentum
$0 = \frac{M}{2}v_{1} - \frac{M}{2}v_{2}$
$v_{1} = v_{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathrm{\Delta}{mc}^{2} = \frac{1}{2}.\frac{M}{2}v_{1}^{2} + \frac{1}{2}.\frac{M}{2}v_{2}^{2}\ \ \ \ldots(ii)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathrm{\Delta}{mc}^{2} = \frac{M}{2}v_{1}^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{2\mathrm{\Delta}{mc}^{2}}{M} = v_{1}^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{1}\ = \ c\sqrt{\frac{2\mathrm{\Delta}m}{M}}$