An alpha$-$particle collides with an oxygen nucleus which is initially at rest. The alpha$-$particle is scattered at an angle of $62\mathrm{.}8$ degrees from its initial direction of motion, and the oxygen nucleus recoils at an angle of $50\mathrm{.}3$ degrees on the other side of this initial direction. What is the ratio, for alpha$-$particle to oxygen nucleus, of the final speeds of these particles? The mass of the oxygen nucleus is four times that of the alpha particle.