In the figure shown, a ball is released from the smooth track. If the ball strikes the horizontal surface of the track and bounces off, it again strikes the horizontal surface at some distance R from B and rises to a height maximum of h' above the surface (If the coefficient of restitution for the collision is e) :-

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At B the speed is v = 2 g h ​ at 6 0 ∘ : v x ​ = 2 v ​ , v y ​ = 2 3 ​ v ​ ; after the bounce v y ​ → e 2 3 ​ v ​ . R = v x ​ ⋅ g 2 ( e 3 ​ v /2 ) ​ = 3 ​ e h , maximum at e = 1 - (B) true, (A) false. h ′ = 2 g ( e 3 ​ v /2 ) 2 ​ = 4 3 e 2 h ​ ≤ 4 3 h ​ - (C) true; at e = 1 , h ′ = 4 3 h ​  = h - (D) false. Answer: (B), (C)

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