Blocks A $($mass $7\mathrm{.}00$ kg$)$ and B $($mass $10\mathrm{.}50$ kg$)$ move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at $5\mathrm{.}00$ 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 A$.$

A$.$ Find the maximum energy stored in the spring bumpers.

Express your answer in joules.

B$.$ Find the velocity of A at the time when the spring energy is maximum.

Express your answer in meters per second.

C$.$ Find the velocity of B at the time when the spring energy is maximum.

Express your answer in meters per second.

D$.$ Find the velocity of block A after they have moved apart.

Express your answer in meters per second.

E$.$ Find the velocity of block B after they have moved apart.

Express your answer in meters per second.