Consider the search for proton decay in a water Cherenkov detector. The refraction index is n=1.33. Find

(1) the minimum velocity of a charged particle for emitting radiation,

(2) the minimum kinetic energy for an electron and a K meson to do so, and

(3) determine whether the charged particle in the decays p → e⁺ + π⁰ and p → K⁺ + ν is above the Cherenkov threshold.