A deuteron of mass M moving at speed v collides elastically with an...

A deuteron of mass M moving at speed $v$ collides elastically with an $\boldsymbol{\alpha}$ - particle of mass 2 M , initially at rest. The deuteron is scattered through $90^{{}^{{}^{\circ}}}$ from initial direction of its motion with speed $V_d$ while the $\boldsymbol{\alpha}$-particle is scattered with speed $V_\alpha$ at an angle $\theta$ from the initial direction of motion of deuteron. Then