A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. If the ratio of the velocities of the sphere after collision is $\frac{{\mathrm{v}}_{\mathrm{A}}}{{\mathrm{v}}_{\mathrm{B}}} = \frac{1-\mathrm{e}}{1+\mathrm{e}}$ where e is the coefficient of restitution, what is the initial velocity of spheres A with which it strikes?

• A

  ${\mathrm{v}}_{\mathrm{A}}+{\mathrm{v}}_{\mathrm{B}}$

• B

  ${\mathrm{v}}_{\mathrm{A}}-{\mathrm{v}}_{\mathrm{B}}$

• C

  ${\mathrm{v}}_{\mathrm{B}}-{\mathrm{v}}_{\mathrm{a}}$

• D

  $\frac{({\mathrm{v}}_{\mathrm{A}}+{\mathrm{v}}_{\mathrm{B}})}{2}$