Maximum angle of deflection after collision

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The discussion focuses on a collision between two equal mass spheres, where sphere A strikes sphere B obliquely. The relationship between the angles of deflection before and after the collision is expressed through the equation cotβ=((1-e)cotα)/2, where e represents the coefficient of restitution. The user expresses confusion about determining the maximum angle of deflection for sphere A, suggesting that the angle might not always be maximized when α varies. They propose that the condition tan^2 α=(1-e)/2 could indicate the maximum deflection angle. The conversation highlights the complexities of applying conservation laws and the coefficient of restitution in collision scenarios.
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Homework Statement



A smooth sphere A impinges obliquely on a stationary sphere B of equal mass. The directions of motion of sphere A before impact and after impact make angles α and β respectively with the line of centres at the instant of impact.

show that cotβ=((1-e)cotα)/2

where e is the coefficient of restitution.
Find in terms of α and e, the tangent of the angle through which the sphere A is deflected, and show that, if α is varied, this angle is the maximum when

tan^2 α=(1-e)/2

Homework Equations


conservation of momentum
coefficient of restitution law



The Attempt at a Solution


I have no problem with first part but the second part seems weird. I think its possible that tan^2 α<(1-e)/2. But anyway using this equation α + β always makes 90 degree. I am wondering if this makes the maximum angle of deflection. but i think they can be less than 90 to make much greater angle of deflection. Please explain it to me.
 
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