Past exam of the mathematics course of the University of Cambridge / 2001 / ib / Paper 4 / 18F / a / Solution

Conservation of momentum in the parent's rest frame gives $p_A+p_B=0$. Equal daughter masses and the relativistic energy-momentum relation then give equal daughter energies. Energy conservation fixesUsing $E^2=p^2{c}^2+m^2{c}^4$ and the specified direction of A,The velocities follow from $v=p{c}^2/E$:These are spatial momenta in the original inertial frame. For positive daughter rest mass, $m<M/2$ gives $0<V<c$.