Problem 1.161

A cannon of mass \(M\) starts sliding freely down a smooth inclined plane at an angle \(\alpha\) to the horizontal. After the cannon covered the distance \(l\), a shot was fired, the shell leaving the cannon in the horizontal direction with a momentum p. As a consequence, the cannon stopped. Assuming the mass of the shell to be negligible, as compared to that of the cannon, determine the duration of the shot.