In a game of snooker, two balls of identical mass and radius collide on a horizontal table. A white ball moving at a speed $1\mathrm{.}5$ m$/$s parallel to the x$$axis collides off$-$centre with a stationary red ball. After collision, the red ball travels away at an angle of $25$ degrees from the x$$axis$,$ on the positive$-$y side.

Assuming the collision is perfectly elastic $($conserves momentum and kinetic energy$),$ calculate the velocity vectors of both balls after the collision.