A $1\mathrm{.}2$ kg billiard ball collides with another $1\mathrm{.}3$ kg ball at rest. After the collision, the $1\mathrm{.}2$ kg ball moves at a speed of $0\mathrm{.}6$ m$/$s at $15$ degrees from its original direction, while the $1\mathrm{.}3$ kg ball moves at $0\mathrm{.}4$ m$/$s at $340$ degrees from the horizontal. Determine the initial velocity of the $1\mathrm{.}2$ kg ball.