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 $$\vec{u}_0 = u_0 \hat{x}$$ and falls on the ground at a distance $$d$$ from the building making an angle $$\theta$$ with the horizontal. It bounces off with a velocity $$\vec{v}$$ and reaches a maximum height $$h_1$$. The acceleration due to gravity is $$g$$ and the coefficient of restitution of the ground is $$1/\sqrt{3}$$. Which of the following statement(s) is(are) correct?