Find the duration of shot

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Homework Statement

A cannon of mass M starts sliding freely down a smooth inclined plane at an angle α 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.

Homework Equations

Kinematics Equations
Conservation of Momentum

The Attempt at a Solution

Acceleration of cannon along incline = $gsinα$
Distance covered = l
Initial Velocity = 0
So final velocity of the cannon (v) = $\sqrt{2glsinα}$
If I take X-axis along the incline and Y-axis perpendicular to it
$\vec{p}_{i}=Mvcosα$
$\vec{p}_{f}=0$ (Since cannon stops)
Since I have to find duration of shot so that means I have to find the time interval during which the momentum of the cannon changed. Am I right with this assumption or does that means something else? If I'm right then how do I find it?