$5.($Exercise; Section $11\mathrm{.}5)$Two dogs are sitting on a raft $($mr$=13$ kg$)$ floating motionless in the middle of a lake. Simultaneously, the first dog $($m$1=21$ kg$)$ jumps off the raft due North at a speed of $2\mathrm{.}5$ m$/$s while the second dog $($m$2=32$ kg$)$ jumps off the raft at a speed of $3\mathrm{.}7$ m$/$s due East.$$

a$.$At what speed is the raft moving immediately after the dogs jump off?