Two particles \(A\) and \(B\) are placed side by side on rough horizontal ground, and are simultaneously projected along the ground in the same direction with speeds \(\quantity{14}{m\,s^{-1}}\) and \(\quantity{21}{m\,s^{-1}}\) respectively. \(A\) comes to rest after travelling \(\quantity{70}{m}\), and \(B\) after travelling \(\quantity{35}{m}\). Calculate the coefficient of friction between each particle and the ground, and show that the times for which the particles are in motion are in the ratio \(3:1\).
Show also that \(A\) passes \(B\) before either particle comes to rest, and calculate the speed of each particle when this happens.
Take \(g\) to be \(\quantity{9.8}{m\,s^{-2}}\).
