An alpha particle collides with an oxygen nucleus, initially at rest. The alpha particle is scattered at an angle of $64.0^{\circ}$ above its initial direction of motion and oxygen nucleus recoils at an angle of $51.0^{\circ}$ below this initial direction. The final speed of the oxygen nucleus is $1.20 \times 10^{5} \mathrm{~m} / \mathrm{s}$. What is the final speed of the alpha particle? (The mass of an alpha particle is $4.00 \mathrm{u}$ and the mass of an oxygen nucleus is $16.0 \mathrm{u}$.)
