Two heavy metallic plates are joined together at $90°$ to each other. A linear sheet of mass $30 kg$ is hinged at the line $AB$ joining the two heavy metallic plates. The hinges are frictionless. The moment. of inertia of the laminar sheet about an axis parallel to $AB$ and passing through its centre of mass is $1.2 kg-m^2$. Two rubber obstacles $P$ and $Q$ are fixed one on each metallic plate at a distance $0.5 m$ from the line $AB$. This distance is chosen so that the reaction due to the hinges on the laminar sheet is zero during the impact. Initially the laminar sheet hits one of the obstacles with an angular velocity $1 rad/s$ and turns back. If the impulse on the sheet due to each obstacle is 6 N-s.

After how many impacts does the laminar sheet come to rest?