Problem 2.99

The velocity distribution of molecules in a beam coming out of a hole in a vessel is described by the function $F(v)=A v^{3} \mathrm{e}^{-m v^{2} / 2 k T}$, where $T$ is the temperature of the gas in the vessel. Find the most probable values of (a) the velocity of the molecules in the beam; compare the result obtained with the most probable velocity of the molecules in the vessel; (b) the kinetic energy of the molecules in the beam.