$3.[10$ Marks$]$ Two field hockey players slam into one another, clutch one another, and slide off together on a slick muddy field. The first player has a mass of $52\mathrm{.}0$ kg and is running due south at $\backslash (8\mathrm{.}00\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ when she hit the other player. The second player has a mass of $47\mathrm{.}0$ kg and she is running at $\backslash (7\mathrm{.}00\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at $\backslash (22\mathrm{.}0^\{\backslash$circ$\}\backslash )$ north of east just before the collision.

$($a$)$ Sketch a large, appropriate, well$-$labelled, vector diagram.

$($b$)$ What is the speed and direction of the players just after the collision?