A slide with a frictionless curved surface which becomes horizontal at its lower end is fixed|MCQ05

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3ℎ from the ground, as shown in the figure. A spherical ball of mass 𝑚 is released on the slide from rest at a height ℎ from the top of the terrace. The ball leaves the slide with a velocity 𝑢0 = 𝑢0 𝑥̂ and falls on the ground at a distance 𝑑 from the building making an angle 𝜃 with the horizontal. It bounces off with a velocity v and reaches a maximum height ℎ1. The acceleration due to gravity is 𝑔 and the coefficient of restitution of the ground is 1⁄√3. Which of the following statement(s) is(are) correct?
(A) u0 = √2𝑔ℎ𝑥̂ (B) v = √2𝑔ℎ(𝑥̂ − 𝑧̂) (C) 𝜃 = 60° (D) 𝑑/ℎ1 = 2√3
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