impulse = change in momentum consider the angle of the polygon = @.
i am considering the moment in which the particle goes from the top most edge to the subsequent edge. let the initial velocity be u i => initial momentum = mu i final momentum = mu cos (180 - @) i + mu sin(180 - @) (-j) = -mu cos@ i - mu sin @ j
=> change in momentum = -(mucos @ + mu) i - mu sin @ j => magnitude = mu root(2(1+cos@) ) = mu sin(@/2)
sunstitute @=pi(2n-2)/2n
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