Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei. The energy of the incoming helium nucleus was 8.00 × 10-3 J, and the masses of the helium and gold nuclei were 6.68 × 10-27 kg and 3.29 × 10-25 kg, respectively (note that their mass ratio is 4 to 197).

(a) If a helium nucleus scatters to an angle of 120o during an elastic collision with a gold nucleus, calculate the helium nucleus's final speed and the final velocity (magnitude and direction) of the gold nucleus.

(b) What is the final kinetic energy of the helium nucleus?