Two identical buggies move one after the other due to inertia (without friction) with the same velocity `v_0`. A man of mass m rides the rear buggy. At a certain moment the man jumps into the front buggy with a velocity u relative to his buggy. Knowing that the mass of each buggy is equal to M, find the velocities with which the buggies will move after that.

Options

A. `v_("rear")=v_(0)+(m)/(m+M)u`
B. `v_("rear")=v_(0)-(m)/(m+M)u`
C. `v_("front")=v_(0)+(m)/((m+M)^(2))u`
D. `v_("front")=v_(0)-(m)/((m+M)^(2))u`