Blocks A $($mass $5\mathrm{.}00$ kg $)$ and B $($mass $7\mathrm{.}00$ kg $)$ move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at $2\mathrm{.}00$ m$/$s $.$ The blocks are equipped with ideal spring bumpers. The collision is head$-$on$,$ so all motion before and after the collision is along a straight line. Let $+$x be the direction of the initial motion of block A $.$