Deflecting a moving disc to a target point

A disc of radius $r_1 = 2$ cm and mass $m_1 = 100$ grams (shown in red) has its center initially (at $t = 0$ ) at the point $P_1 = (14, -2)$ cm, and moving on the $x y$ plane with a velocity of $v_1 = ( - 0.5, 0.4 )$ cm / sec. You have another disc of radius $r_2 = 1$ cm and mass $m_2 = 200$ grams (shown in green), initially having it center at the point $P_2 = (-5, -5)$ cm. You shoot this second disc in a certain direction at a speed of $0.9$ cm / sec, such that it collides (elasticly) with the first disc, and deflects it, so that its center passes through a target point $P_3 = (10, 12)$ cm (shown in red).

Find the angle $\theta$ (with the positive x-axis, in degrees) that you should point the second (green) disc at, to satisfy the requirement of passing the center of the red disc through the target point.

Note: You may need to utilize an iterative numerical technique like Newton-Raphson single variable method.