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 cannon, determine the duration of the shot.

Explanation

Velocity of cannon as well as that of shell equals `sqrt(2glsin alpha)` down the inclined plane taken as the positive x-axis. From the linear impulse momentum theorem in projection form along x-axis for the system (cannon+shell) i.e. `Deltap_x=F_xDeltat`:
`pcos alpha-Msqrt(2glsin alpha)=Mgsin alphaDeltat` (as mass of the shell is negligible)
or, `Deltat=(pcosalpha-Msqrt(2glsin alpha))/(Mgsin alpha)`