A $2$kg brick slides along a frictionless horizontal surface, moving at $15$ m$/$s$.$ It strikes a stationary block $(4\mathrm{.}5$ kg$)$ initially stationary. The two lock together and slide along horizontally a little bit further, before rising up an incline, and reach some height H before stopping. Calculate:

 a$)$ the speed that the brick and block move off with after colliding and locking together.

 b$)$ The height H the block and brick combination reach after sliding up the incline and coming to rest. There is no friction in this problem.